Aptitude - Time and Work - Discussion

4. 

A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:

[A]. 20 days
[B].
22 1 days
2
[C]. 25 days
[D]. 30 days

Answer: Option B

Explanation:

Ratio of times taken by A and B = 1 : 3.

The time difference is (3 - 1) 2 days while B take 3 days and A takes 1 day.

If difference of time is 2 days, B takes 3 days.

If difference of time is 60 days, B takes 3 x 60 = 90 days.
2

So, A takes 30 days to do the work.

A's 1 day's work = 1
30

B's 1 day's work = 1
90

(A + B)'s 1 day's work = 1 + 1 = 4 = 2
30 90 90 45

A and B together can do the work in 45 = 22 1 days.
2 2


Rajender said: (Jun 16, 2010)  
Please tell me how you have calculated differece of time 2 days.

Sundar said: (Jul 5, 2010)  
Hi Friends!

The statement "A is thrice as good as workman as B" states that, If A complete a work in 1 day, B will take 3 days to complete the same work.

Therefore, if A takes 1 day, B takes 3 days, the time difference is 2 days.

If the time difference is 2 days, B takes 3 days to complete the work.

Similarly if the time difference is 60 days, then B takes (3/2*60) = 90 days.

Then A takes 90 - 60 = 30 days to complete the work.

It is very simple man.

Kumar said: (Jul 5, 2010)  
Hi Guys,

Let me do the same thing with different values.

Given statement : "A is thrice as good as workman as B"
Time difference : 60 days.


If B takes 12 days to complete a work, A will take only 4 days to complete the same work.

So, B takes 12 days whereas A takes 4 days only (because A is thrice as good as B).

Here time difference is 12 - 4 = 8 days.

If the time difference is 8 days, B takes 12 days.

Similarly if the time difference is 60 days, then B takes (12/8 * 60) = 90 days.

...Rest thing you can understand from the explanation part.

Bharathi said: (Jul 9, 2010)  
Dear Friends,

In this question atlast we got (a+b)'s 1 day work=2/45.

How it is changed to be an A and B are together can do the work in 45/2.

Nagu said: (Jul 12, 2010)  
Hi Bharathi,

If A takes 10 days to complete a work means
A's one day work is 1/10

so complete this work A takes 10/1 days is same as 10 days

Sat the same way (A + B)'s 1 day's work 2/45 means

They will take 45/2 = 22 1/2 days

I think you got my point

have a nice day

Sheetal said: (Aug 3, 2010)  
Hi Guys,

Don't be confused in data given in question.

I have one short cut to solve such kind of question.

A is K times as good a worker as B & takes X days less than B to finish the work. Then the amount of time required by A & B working together is K * X / K'S SQUARE - 1.

SO IN QUESTION K IS 3. X IS 60. SO PUTTING THE VALUES IN ABOVE MENTIONED FORMULA.

K * X / K'S SQUARE - 1
=3 * 60 / 9 - 1
=3 * 60 / 8
=180 / 8
=22.5 DAYS

AS MENTIONED OPTION B.

I HOPE U WILL UNDERSTAND THIS THING & WILL APPLY IN QUESTION BASED ON THIS.

All the best. Have nice day!

Sangeetha said: (Aug 4, 2010)  
Oh thanks sheetal

Indhu said: (Sep 1, 2010)  
Hi friends,.

Though content is big it is easy to understand.

Work done by A as compared to B=3:1.

Time taken by A as compared to B=1:3.

So, time difference is 2.

A will finish the work 60 days lesser than B.

Therefore time difference is 60.

Time taken for A = 60/2 = 30.

Hence time taken for B=3* time taken by A = 90.

If A+B can do a piece of work in n days, then (A+B) 's 1day's work=1/n.

Working together (A+B) 's one day work = (1/30) + (1/90) =2/45.

If (A+B) 's 1day's work=1/n, then A+B can finish the work in n days.

Therefore total time taken = 45/2= 22. 5 Days.

Prashant said: (Sep 15, 2010)  
Suppose B takes x days to finish the work and then according to question A will take (60-x) days to work. in question the ratio of time taken is 1:3 therefore

1/3= (60-x)/x
x=45

So A can complete the work in (60-x)=(60-45)=15 days

So (A+B) one day's work
=(1/15 + 1/45)
=4/45

So (A+B) complete the work in 45/4 = 11 1/4 days.

Sugumaran said: (Sep 22, 2010)  
Ratio of time taken=1:3

A finish the work in 60 days and B in x days.

1:3::60:x
x=180 days

So,

A and B 1'days work 1/60+1/180=45 days

Is it correct or not?

M.Atul said: (Sep 23, 2010)  
@Sugumaran please read carrefully problem. Though you have got same answer but it doesn't satisfied second condition that differnce in day should be 60 not 120.

Priya said: (Sep 23, 2010)  
Please tell me why we are taking 3/2 to multiply with 60. Please explin me.

Harsha said: (Oct 13, 2010)  
A clear approach:

Given: A's time taken:B's time taken=1:3

So A's proportion of time taken=1/(1+3)=>1/4*some x
B's proportion of time taken=3/(1+3)=>3/4*some x

As it is said that difference of time is 60 days

B's time-A's time=60
=> 3x/4-x/4=60
=>x=120

So A's proportion of time taken =x/4=120/4=30 days
B's proportion of time taken =3x/4=3*120/4=90 days

A's 1 day's work = 1/30
B's 1 day's work = 1/90
(A + B)'s 1 day's work = (1/30 + 1/90)= 4/90=2/45

A and B together can do the work in 45/2 = 22 1/2 days.

Naveen said: (Oct 26, 2010)  
Hi, in prashanth answer, he equals the ratio 1/3 to 60-x/x but it actually x-60/x.

Shilpi said: (Nov 18, 2010)  
Can you pls teach me this equation
1/30+1/90=4/90

Ashirwad said: (Nov 27, 2010)  
HI FRIENDS THIS IS THE simplest method for solving this type of que....
K*S/(A^2-1)

where S=DAYS FOR FINISHING WORK(60 GIVEN IN QUE)
K=3 GIVEN IN QUE

Ashirwad Dubey said: (Nov 28, 2010)  
Hi friends
k*x/(k^2-1)
k=3
x=60 given in que
ok friends

Vikas said: (Dec 29, 2010)  
I didnt understand how did we get that (3/2)*60 ?

Showry said: (Jan 5, 2011)  
Hi Friends,

A:B=1:3 time taken.........since A is 3 good as B

A takes 60 days less than B
B-60:B=1:3............
i.e B-60/B=1/3..... B=90 days.... A=30......

(A+B)'s one day work (1/30+1/90) = (2/45)

Total work by (A+B) is 45/2 i.e 22 1/2.............

Gowri said: (Jan 8, 2011)  
kl/(k)^2-1
k=3
l=60
3*60/(3)^2-1
=45/2
=22.5

Nagarjun said: (Jan 13, 2011)  
@Vikas

Its just cross multiplication.
If the difference is 2 days then b takes 3 days
If the difference is 60 days then b takes x days

Hence, x= (60*3)/2.

I think you got it now.

Naresh Kumar said: (Jan 18, 2011)  
Thank you guys.

Malini said: (Jan 19, 2011)  
Sheetal thanks a lot dear. This short cut is very much easy.

Baskar said: (Jan 21, 2011)  
@bharathi
i think u r in confusion..
just know dat
work = day..
1 day = 2/45 works..
in ques ask abt "work"?
den cross mul
1 work = 45/2 days..
now u got it

G.P. said: (Feb 10, 2011)  
SIMPLE AND BEST WAY
since a is thrice better than b
hence a:b=1:3
similarly a takes 60 days less than b
hence a:b=(b-60):b=1;3
cross multiplication n we get
3b-180=b hence b=90days hence a=30days
1/90+1/60=4/90 hence total daysreciprocal 90/4=45/2

Nishant said: (Feb 10, 2011)  
@ G.P.

Thanks. I like the way you solve it.

Balaji said: (Feb 19, 2011)  
Showry you explained superbly.

Prathyusha said: (Feb 28, 2011)  
SIMPLE AND NICE EXPLANATION!... @KUMAR

Vani said: (Mar 18, 2011)  
Showry's explanation is good.

Siva said: (Apr 21, 2011)  
Hi Guys,
I think following simple method (alternate) will make you more clear,

A can complete work in N days => A's 1day work = (1/N)----1
B can complete work in n days => B's 1day work = (1/n)----2

Given data,
A thrice as B so , A=3B
A complete work 60 days less than B so, (N=n-60)

Apply in 1 & 2

A's 1day work = (1/(n-60))-----3
B's 1day work = (1/n)--------4

we know that A=3B ; B=(1/n) so,Apply B in A we get[A=3/n]

Apply in 3

3/n=(1/(n-60))
by solving,
3n-180=n
n=90
so, B can complete work in 90 Days => B's 1 Day work =(1/90)
we know that N=n-60,
so, A can complete work in 30 Days => A's 1 Day work = (1/30)

(A+B) 1 Day work = (1/30 + 1/90)
by solving we get,
A+B 1 Day work = 2/45,
so A and B together can complete work in 45/2 Days.

Hindu said: (Jun 25, 2011)  
Hai sheetal your shortcut method helps lot to understand so quickly its really super.

Naveen Kumar said: (Jul 1, 2011)  
Hi friends, Here is a simple technique to calculate the above problem....

Given,

If the If difference of time is 2 days, B takes 3 days.
If difference of time is 60 days, B takes......?

We can represent the above relation like this,

2------->3
60------>....?

By cross multiplying the above terms we will get... 60*3/2 = 90.

Note:- Always individual term should come in the denominator.

By applying the above procedure you can solve any problem of this type....

I think this technique will help you while doing with this type of problems...

Abdul said: (Jul 9, 2011)  
Hey Siva your way of solving is fantastic and understandable! Thanks.

Jezan said: (Jul 17, 2011)  
According to this question if A is x, B will be x+60
1/3=x/x+60
3x=x+60
2x=6
x=30
A+B'S ONE DAY WORK=1/30+1/90=2/45
SO WHOLE WORK S= 45/2( UPSIDE DOWN)
22.5 DAYS.
HOPE ALL LL GET DIS

Jaswinder Singh said: (Aug 14, 2011)  
Ratio of times taken by A and B = 1 : 3. or 1x:3x
so, we say
3x-1x=60,
2x=60,
x=30, so A will 30 day to complected a work,
B will be complete the work ie 3x, 3(30)=90days,
(A+B) 1 Day work = (1/30 + 1/90)
by solving we get,
A+B 1 Day work = 2/45,
so A and B together can complete work in 45/2 Days.

Sharan said: (Aug 21, 2011)  
@Jaswinder singh: I understood your explanation man. Thanks.

Sundar said: (Aug 22, 2011)  
@All (Must read if you have any doubts)

If B takes 3 days then A takes 1 day to complete the task.

Time taken Ratio => A : B = 1 day : 3 days.

1 3 (difference is 2)

10 30 (diff 20)

30 90 (diff 60) <= Here diff is 60 days, So this is the correct ratio to be used in calculation, since it was mentioned in the given question.

A alone can finish the task in 30 days.
B alone can finish the task in 90 days.

Work done by A alone in 1 day = 1/30
Work done by B alone in 1 day = 1/90

Work done by A and B in one day (1/30 + 1/90) = 3+1/90 = 4/90

The no. of days required to complete the task by A and B is
= 90/4
= 22.5 days.

////**** Important Note: ****////

We cannot take other ratios like 1:3, 10:30, 40:120, 60:180 for the calculation. Since the diff is mentioned as 60 days.

Because, it will give different answers for each different ratios used for calculation.

If we take 1:3 => (1/1 + 1/3) = 4/3

If we take 10:30 => (1/10 + 1/30) = 4/30

If we take 40:120 = (1/40 + 1/120) = 4/120

If we take 60:180 => (1/60 + 1/180) = 4/180 ... so on.

I hope this will help you. Have a nice day!

Deepti said: (Aug 25, 2011)  
It is not so big and easy to understand.

let work done by B in 1 day = 1/x
so work done by A in 1 day = 1/(x-60)
1/(x-60) = 3/x
so x = 3x - 180
x = 90
work done by A and B in 1 day is 30 and 90 respectively
work done by both together in 1 day = 1/30 + 1/90 = 2/45.
total work done = 45/2

Harsha said: (Sep 1, 2011)  
Easy method :

A can completed in x days
B can in 3x days then

A = B-60 (A can do in 60 days less than B )

=> x=3x-60 => x= 30 =>

A=30, B=90

Then together work done is (1/30+1/90) = 2/45.

Finally total work done is 45/2.

Pinky said: (Sep 10, 2011)  
@Sheetal superb explanation.

Praveen said: (Sep 16, 2011)  
Nice exp. Harsha.

Nitin Singla said: (Sep 23, 2011)  
Hey its simple to understand.
Days taken by B = x
Days taken by A= x - 60
Their time taken proportio is 1:3
so,
x - 60/ x = 1/3
x=90;
So A will do the work in = 30 days
abd B in 3x= 3*30=90 days,
and u can find their 1 day's work and ad it.
Simple :)

Srinivas said: (Sep 25, 2011)  
Hi friends,

Given A:B=1:3

Therefore B=3A--------equation 1

let B can do a work in x days.

then A can do the same work in (x-60) days.

then B=3A
x=(x-60)3

therefore x=90 days

therefore B can do a work in 90 days.

and A will do a work in 90-60=30 days.

Pavethra said: (Sep 29, 2011)  
I tell that A is thrice as good as B so it should be 3:1 na.

Am I right?

Sunil Reddy said: (Oct 4, 2011)  
We can use a simple formula here:[(KL)/k squqre-1)]

-->here K=3(efficiency),L=60(time) so (3*60/(3*3)-1)=>180/8=221/2

Vinod Reddy said: (Nov 7, 2011)  
THANK U SHEETAL,your short cut method is simply super.there is no words to say

Sundar said: (Nov 18, 2011)  
If difference of time is 60 days 3*60/2 = 90 days.

I can't get this step?

Please explain.

Riyaz said: (Nov 23, 2011)  
Ratio of times taken by A and B = 1 : 3.

That is If A takes 1 day B takes 3 days
Time Difference is 3-1 = 2 days

Here is the tricky part :
If A takes 1/2 day B takes 3/2 days
Time Difference is 3/2 - 1/2 = 1 days

When time difference is 60 days (Just mulitply by 60)
A takes 60/2 and B takes 3*60/2

So, A takes 30 days to do the work.
and B takes 90 days to do the work.

A's 1 day's work = 1/30
B's 1 day's work = 1/90

(A + B)'s 1 day's work = (1/30 + 1/90)= 4/90 = 2/45

A and B together can do the work in 45/2 = 22+1/2

Anu said: (Nov 27, 2011)  
Awesome explanation HARSHA

Brajesh Anuragi said: (Nov 28, 2011)  
Thanks Showry for given the simple and correct ans.

Gauarv said: (Dec 27, 2011)  
Thanks harsha.

Neeraj said: (Jan 8, 2012)  
A will finish the work 60 days lesser than B.

What is it mean please explain?

Abhay said: (Jan 10, 2012)  
@Neeraj-A will finish the work 60 days lesser than B,means if B takes 60 days to complete the work,A takes 1 day.

Sureshkumar said: (Jan 19, 2012)  
Another easy way 2 find out:

1st put the ratio i.e.1:3(A:B)
2nd the condition given here is A can work less than 60 days

So, find out the probability that matches with the ratio condition(A&B must be difference 60 here) for eg:let we take as A as 20 therefore B must be 60(here we get the difference as 40 only)according to 1:3 which cant satisfy

The given condition(A less than B by 60 days) suppose you take A as 30 means you get B as 90 which is greater than 60 days
of A....A=30 B=90 A's 1 day work=1/30

B's 1 day work=1/90 A+B's 1 day work =1/30+1/90=4/90 here they are not given to find out as 1day work...so take as 90/4=22.5 <==> 22(1/2).

Varma said: (Jan 26, 2012)  
Nice formula @Sheetal.

Aarush said: (Feb 16, 2012)  
Thanks sheetal.

Raman(Uiet,Kuk) said: (Feb 17, 2012)  
Guys check this out and don't be confused....
as we know A is 3 time better than B and A takes 60 days less than B so, time taken by A: time taken by B= 1:3
= b-60:b ( suppose time by B is b)
by cross multiply, 3b-180=b
i.e. b=90 so time taken by B=90
and time taken by the A is=90-60= 30

Tabish said: (Feb 18, 2012)  
@sheetal
do not able to understand how you get that formula to calculate the time i.e.
K*X/K^2-1

Kapil said: (Feb 20, 2012)  
Nic Explanation. . .Sheethal. . .

Shro said: (Feb 20, 2012)  
Indhu very easy simple explanation as per the question.
Good :) thanku :)

Sindhu said: (Feb 23, 2012)  
HI,
This method I feel to be quiet easier.
A is thrice as good as workman as B.
therfore,
A=3B -(1)
finish a job in 60 days less than B
1/B=60+1/A -(2)
i.e B`s One day work = A`s one day work + 60 days.
Solve (1) & (2)
we will get
A= 90;
From (1)
B=A/3
=> B= 30.

(A+B)`s 1 day work = 1/90+1/30
=2/45
=22 1/2 days

Iyappan said: (Apr 12, 2012)  
Naveen kumar your explanation is beautiful for me.

Sanchi said: (Jun 3, 2012)  
Very simple way.
3A=1B
B takes x days.
3 (x-60) =x
3x-x=180
X dats is B=90, A=30.
Now,
1/90+1/30=22. 5.

Nitin Singh Parihar said: (Jul 5, 2012)  
Let B do the work in 'x' days.

So, A will take (x-60) days.

Now, ratio of A:B=1:3 (given in ques).

So, 1/3=x-60/x.

=> x=90 (B's 1 day work).

So, A's work=30 days.

Working together=1/30+1/90.

=45/2 days.

Easy and simple.

Akansha said: (Aug 7, 2012)  
B takes 3 times more days than A.

i.e. B=3A.

So. B-A=60.

3A-A=60 =>.

A=30.

B=90.

Now calculate 1 day work of A and B.

Sunny said: (Aug 26, 2012)  
A is thrice as good as workman as B means 1:3(Ratio)
Therefore A is able to finish a job in 60 days less than B
So A= 1/60 and B=1/60 .....(Given)
According to the ratio
A=1/60 B=1/3*60 (As we are calculating by days)
So Now A = 1/60 < B = 1/90 (A finishes work less than B)
Working together, they can do it in:
1/A+B = 1/60 + 1/90 (As we are calculating by days))
1/A+B = 2/45
So
A+B = 45/2 Days
Option (B) is the correct ans

Vidya said: (Aug 27, 2012)  
Can you please solve this using unitary method. Its b'coz I follow that method.

Anji said: (Sep 4, 2012)  
Let the time taken by A be x days,
then time taken by B will be 3x days.
Given that,
time taken by A to finish the work = time taken by B -60
i.e, x=3x-60
=> x=30.
Therefore, time taken by A to finish the work is 30 days.
so B takes 90 days.
Now ,work done by A & B in 1 day=1/30 + 1/90
=4/90
=2/45
Time taken by A & B to complete the work=45/2 days
=22 1/2 days

Sanjeev said: (Sep 11, 2012)  
#include<stdio.h>
void main()
{
float a,b;
int c,d;
printf("enter ratio of A : B\n");
scanf("%f",&a);
printf("enter no of days lesser than B by A to complete work\n");
scanf("%f",&b);
c=ab/(a-1);
d=c-b;
printf("no of days to complete work by A and B is %d",(c*d)/(c+d));
}

Prabha said: (Sep 24, 2012)  
If difference of time 2 days B takes 3 days

Similarly why don't we take difference of time 60 days B takes 60*3 is 180 days. Please explain to me ?

Joshi Sir said: (Nov 21, 2012)  
Friends, don't make it complex: Here we go.

Ratio of time taken by A & B = 1:3

And A takes 60 days less then B

Suppose, days taken by B = x then days taken by A = (x - 60)

Thus,

A : B = (x - 60) : x
1 : 3 = (x - 60) : x
1/3 = (x - 60) / x
X = 3 (x - 60)
X = 3x - 180
180 = 3x - x
180 = 2x
X = 180 / 2 = 90

Hence,
Days taken by B = x = 90 days
Days taken by A = (x - 60) = 90 - 60 = 30 days

1 day work of A and B = 1/30 + 1/90
= 4/90
= 2/45

So,
Total days taken by A & B to complete the work = 45/2 = 22.5 days

Ashutosh said: (Nov 29, 2012)  
Formula-->nx- (n+1) /nx.
4x-4x/3=60 so x=45/2.

Keerthi said: (Jan 10, 2013)  
So by the explanation above we have to take in the ratio 1:3.

Kavya said: (Jan 10, 2013)  
A is twice as good a workmen as B and together they can finish a piece of work in 18days. In how many days will A alone finish the work?

Can we solve the above problem using the formula k*x/k^2-1.

Pankaj said: (Feb 5, 2013)  
Let A takes x days to do the work alone
Therefore days taken by b is (x+60).

Now A is 3 times faster than B
So no.of days taken by A will be 3 times less than B.
So
3*x=(x+60)
2x=60
x=30 days //work done by A
Work done by B=30+60=90 days.

Now we can find work done together
1/30 +1/90 to get the answer.

Monika said: (Feb 11, 2013)  
We have a direct formula for these kind of questions .. i.e.,

Work done together is given by = (m*d)/(m^2 - 1),

Where d is no of days taken by B and m is no of time A is faster than B,
Therefore = (3*60)/(3^2-1) = 22.5.

Praveen said: (Mar 10, 2013)  
@All.

Please refer to Sheetal's response as given below. Its the best and easiest way to solve such questions.

PS:Thanks sheetal.

"A is K times as good a worker as B & takes X days less than B to finish the work. Then the amount of time required by A & B working together is K * X / K'S SQUARE - 1.

SO IN QUESTION K IS 3. X IS 60. SO PUTTING THE VALUES IN ABOVE MENTIONED FORMULA.

K * X / K'S SQUARE - 1
=3 * 60 / 9 - 1
=3 * 60 / 8
=180 / 8
=22.5 DAYS.

AS MENTIONED OPTION B.

Sridhar said: (Apr 28, 2013)  
Simple way:

A and B ratio 1:3.

Since A finishes 60 days lesser than be A takes 90 days and B takes 30 days.

So per day calculation (1/90+1/30) = 22.5 days.

Vinod Anand said: (May 22, 2013)  
If A is thrice as good as workman B,
Than A=3B ----(1) or B=A/3 --------(2).

If A is finish a job in 60 days less than B.
Than A = B-60.

Put the value of B from Eq.(2).

A = A/3 -60
3A = A-180
2A = 180
than A = 90 Days.

Same Put the value of A in Eq.(2).
B=90/3 = 30 Days.

So Working together (A+B) = 1/90 + 1/30.

A+B = 2/45.
or A+B =45/2 = 22.5 or 22 1/2.

Answer.22 1/2 Days.

Parashar said: (May 31, 2013)  
Simple yaar.

>A is thrice as good as workman as B and therefore is able to finish a job in 60 days=IF B TAKE 90 DAYS THEN A WILL TAKE 30 (60 DAYS LESS).

>1/30 (PLUS) 1/60=4/90==>90/4==>22. 5 SIMPLE.

Thirupathi Malavath said: (Jul 24, 2013)  
Simple method:

Say B completes the work in 'x' days.

Then A will take (x-60) days to finish the work.

Since A is thrice as good as B, 3A=B.

Therefore, 3 (x-60) =x, x=90.

B's 1 day work=1/90, A's 1 day work=1/30.

(A+B) 's 1 day work= (1/90+ 1/30) =2/45.

Therefore, both can finish the work in 45/2 days i.e., 22 1/2.

Ankush Rana said: (Aug 9, 2013)  
A is twice as good as workman B and together they finish a piece of work in 14 days. A alone can finish the work in.

Sam said: (Aug 10, 2013)  
Did they mention that difference of working time is 60 days.

Shivaram Vollala said: (Aug 21, 2013)  
In the given question the ration of capacity of work in day a:b is = 3:1.

So always inverse proportion to capacity and work like the way a and b can do the work ration =1:3 i.e. a's one day work = b's three days work.

So let now finish work together is imagine x.

Ratios of each person a's work = x* 1/4 = X/4. (1).

Ration of b's work = x* 3/4 = 3X/4. (2).

In the given question difference is 60 days.

So 3X/4-X/4 = 60 Days.

Solove ther x we get x = 120.

Now substitute x in (1) and (2).

W e get a's part of one day work = 30 days.

And b's part of one day work = 90 days.

Now solve the.

A and B together work = 1/30+1/90 = 4/90 =2/45.

This is and b together part of work now one day work = 45/2 = 22.5 days.

Sudhanshu said: (Sep 19, 2013)  
Why so many stories I don't know.

Its as simple as this:

A's 1 day's work = x.

B's 1 days work = x+60.

So, total one day's work is.

1/x + 1/x+60 = 1.

And you get x = 30 that is total days required for A to cmplete the work where B's value gets 90 days.

Rest you can solve.

Malay Kanti Bhunia said: (Sep 21, 2013)  
X - 3X = 60.

X = 30.

A done works 30 days and B done the work 90 days.

A work done in 1 day 1/30 part.

B work done in 1 day 1/90 part.

A and B work together in 1 day (1/30+1/90) = 2/45 part.

Time taken in this work 22.5 days.

Jag Parvesh said: (Dec 22, 2013)  
Ratio of times taken by A and B to finish a work is 1 : 3.
A:B=1:3 OR A/B=1/3 or 3A=1B --(1).

B-A = 60.
B-(1/3)B = 60 (Substituting the value of A from eq 1).
3B-B = 180 (Multiply through by 3).
2B = 180.
B = 180/2.
B = 90.
A = (1/3)*90.
A = 30.

So, A can do the job in 30 days.
Therefore, A can do 1/30 of the job per day.

And B can do the job in 90 days.
Therefore, B can do 1/90 of the job per day.

Work they can do per day:
= (1/30) + (1/90).
= (3/90)+(1/90).
= (3+1)/90.
= 4/90.

So the job will take 90/4 days, which is 45/2 or 22.5 days.

M Ahmad said: (Feb 4, 2014)  
A can do the job in x days.
B can same job in 3x days.

3x=x+60 by B.
x=30.

One day work by A and B = 1/30+1/90 = 4/90 = 2/45.

Whole job done by A and B = 45/2 = 22.5 days.

Michael said: (Mar 25, 2014)  
How do we get 4/90 ?

Mancy said: (Apr 12, 2014)  
Hi @Michael,

By taking the L.C.M of 30 & 90 you'll get 90.

Now, here the value become.

=1/30+1/90.
=(3+1)/90.
=4/90.
=2/45.

So, 2/45 is total work done by them,
But we've to find the days.

By formula work to days.

N work = 1/N days.
So, 2/45 = 45/2 days.

Answer = 22.5days.

Sundar said: (Apr 23, 2014)  
Please Tell me how 3/2 has come?

Atul1487 said: (Apr 28, 2014)  
What is need to take time difference?

How will I come to know that I need to calculate time difference?

Venkatesh said: (May 21, 2014)  
Hi friends just read, A's works 3 times than B so work ration 3:1 and time ratio will be 1:3 in the question they ask for time so 3/(3-1)*60=90.

A 3 times better 3/90=1/30(1 days work) B 1/90 1days work together 1/90+1/30=answer.

Poornachandran said: (May 24, 2014)  
Guys,

I'll tell by simple method.
Given, A is thrice of B.

So A = 3B---->(1).
A's 1 day work is A=1/60--->(2).

Substitute (2) in (1),
A=3B.
We get,
3B=1/60.
B=1/180.

In question they asked A+B=how many working days?
We know A and B values.

Add A and B.
1/60+1/180=1/Work days.
Take L.C.M.

3+1/180=1/Work days.
4/180=1/work days.
1/45=1/work days.
Work days=45.

By fraction we can write 22 1/2 days.

Kumar said: (May 26, 2014)  
How its "4/90 " ?

Nithya said: (Jun 24, 2014)  
Lets B takes x days to complete the Work,

Then B 's Capacity ==>1/x.
A is 3 times as good as A so A'S capacity is 3/x.

Then Time Taken by B is = x/1.
Time taken by A is = x/3.

Time difference (x-x/3)=60.

Which gives x = 90.
Time taken By B = 90.
Time taken By A = 30.

(A's Work +B's Work) 1 day Work = (1/30)+(1/90).
= 4/90.

Then Time taken to complete work is 90/4 ==> 22.5 days.

Pranay said: (Jul 13, 2014)  
The work being done by A & B is in ratio of 1:3.

This means if A does a work in 1 day, than B will do this work in 3 days.

Now let suppose this ratio is multiplied by a factor, say x.

Then ratio becomes x:3x.

Now another relation given is that A can do work 60 days faster then B. Mathematically we can write it as.

x=3x-60.

Solving this, we get x = 30.

Hence the ratio becomes 30:60.

Now we can calculate the time taken by them.

Thaha said: (Jul 22, 2014)  
"A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B."

Solution:
*********
'A' able to finish a job in 60 days 'less than B'.
Let A's work is = x days.
Let B's work is = 3x days.
A able to do a work in 60 less than B.

Therefore,

A's work = B's work - 60.
So,
x=3x-60.
Then x=30.

A can complete the work in 30 days.
B can complete the work in 3*30 = 90 days.

A's one day work = 1/30 days.
B's one day work = 1/90 days.
A+B one day work = (1/30)+(1/90) = 4/90 days.
Therefore A and B can finish the work in = 90/4.
So the answer is : Option [B].

Kalyani said: (Jul 28, 2014)  
What is the meaning of taking 3/2 in the problem. What's that ratio about?

Piyasa Dey said: (Aug 20, 2014)  
If A does a work in 1 day.
therefor B does the same work in 3 days since A is thrice as good as workman as B.

Let A completes the work in x days, B will take (x + 60) days more than A takes.

Therefore 1:3 :: x :(x + 60).
Now according to the formula if a:b :: c:d.
Then it is considered as (a * d) = (b*c).

Applying this formula we get 1*(x + 60) = 3*x.
By solving we get x= 30 i.e A takes 30 days to complete the work.
Therefore B will take (30+60)=90 days.

A's one day work = 1/30 days.
B's one day work = 1/90 days.
A+B one day work = (1/30)+(1/90) = 4/90 days.
Therefore A and B can finish the work in = 90/4.

Deepak Patgar said: (Aug 22, 2014)  
Let A completes work in x days.
So no of days taken by B to complete the same work will be 3x days.

A takes 60 days less than B.

So 3x-60 = x.
2x = 60.
x = 30 days (number of days taken by A).
3x = 90 days (number of days taken by B).

Work done by A per day is 1/30.
Work done by B per day is 1/90.

Work done the together in 1 day will be (1/30+1/90) = 4/90.

So work done by them in 10 days will be 40/90.

Work done in 20 days 80/90.

Number of days require to do the remaining 10/90 will be 2.5 days.

Ans = 22.5 days.

Poor Gamer said: (Aug 29, 2014)  
Let A takes x days and B takes 60+x days.
Its given that A takes 1 days when B takes 3 days.

So,
1/3 = x/x+60.

Cross multiply and we get x = 30 i.e A.
X+60 = 30 + 60 = 90 i.e B.

Remaining as usual.

Divyanshu Dwivedi said: (Sep 2, 2014)  
Simple:

A's work = x.
B's work = y = 3x.

Hence acc. to ques.: 3x - x = 60 ;.
x=30 A's.
y=90 B's.

Now.... 1/30 + 1/90 = 1/z.

z = 90/4 Answer.

Mohit Jain said: (Dec 4, 2014)  
Let,

A takes = x days.
B will take = 3x days.

Difference 3x-x = 60.

So 2x = 60.
x = 30 days.

Thus A can do it in 30 days and B in 90 days.

Sumit said: (Dec 8, 2014)  
If difference of time is 60 days, B takes 3/2 x 60 = 90 days.

Please explain this statement.

Prakash said: (Dec 15, 2014)  
But there is not given difference in question they given A finish work in 60 day?

Ankita said: (Jan 12, 2015)  
If B takes y days , A takes (y-60 ) days. Now , their efficiency are A:B = 3x : x.

So total unit of work is 3x*(y- 60 ) man days = x*y man days.

Calculating this we get y = 90. So if B worked for 90 days, A worked for 30 days.

Hence 1/30 + 1/90 = 22 1/2 days :).

Priya said: (Mar 17, 2015)  
No need to do all that simply guess numbers 30 & 90 which is satisfying this then without using pen we can get answer 22.5 days.

Ankita said: (Apr 5, 2015)  
Suppose A takes x days.

Then, B will take 3x days.

From question, 3x-x = 60.

=> x = 30.

=> A takes 30 days and B takes 90 days.

Together they will take = 30*90/30+90.

= 30*90/120.

= 90/4.

= 22.5 or 22 1/2 days (ans).

Aaa said: (Apr 7, 2015)  
Is there a fixed formula for this?

Govardhan Reddy said: (Apr 9, 2015)  
Why were their difference between days? Please explain to me.

Sachin said: (Apr 28, 2015)  
Its very simple.

Suppose B's done work = X day.

Then A's done work = (X-60) day.

Efficiency ratio is.

A : B = 1:3.

(X-60) : (X) = 1:3.

X = 90.

So A's take days = 30.

B's take day = 90.

A's 1 day work = 1/30.

B's 1 day work = 1/90.

(A+B) s 1day work = 1/30 + 1/90 = 2/45.

So together they will take = 45/2.

Raj said: (May 15, 2015)  
Easy lets assume A works total days = X.

So A one day work = 1/X.

B is working 3 times less than A.

So Total days of B is = 3X.

So B Works one day = 1/3X.

Different between total days of B and A is 60.

So 3X-X = 60.

2X = 60.
X = 30.

Now normal maths. Replace X with numbers. You will get answer.

So 1/30-1/90 = 22.5.

Arjun said: (May 18, 2015)  
Can any one give me a easier way using LCM method?

Mohit Agnihotri said: (May 25, 2015)  
Work done ratio (A:B) = 3:1.

And let x be no. of days taken by B.

So, A:B = x-60:x {Given- A finish a job in 60 days less than B}.

Now, (x-60)/x = 1/3.

3x-180 = x => x = 90.

It means A takes 30 days and B takes 90days.

One day work of A and B is 1/30+1/90 = 4/90.

Thus, 90/4 = 22.5 days required to complete the work.

Pratyush said: (Jun 8, 2015)  
Can we do it like this:

a = 3b....(1).

a-b = 60.
3b-b = 60.

2b = 60.
b = 30.

If b = 30 then from 1a = 3x30 = 90.

Now,

= 1/30+1/90.
= 3+1/90.

= 4/90 = 2/45.
= 45/2 = 22.5 days.

Neeraj said: (Jun 11, 2015)  
Shortcut:

A & B together will complete in 6/14/8 = 24/7 days = 3 3/7 days.

Work completed in 3 days. So C's share 3/7 days.

Now 3200/24/7*3/7 = 400.

Rajat Singh said: (Jun 16, 2015)  
Simple solution:

a = 3b.
a-b = 60 (difference of b).

3b-b = 60.
b = 30, a = 90.

So they can together work in 1/30+1/90 = 4/90.

:->22.50.

Megala said: (Jul 2, 2015)  
Please explain last 2 steps.

Surya said: (Jul 11, 2015)  
Simple formula with solution:

(D) n/n2 (i.e n square)-1 = work together.

Details:

D-60, n-3, by putting the formula = (60)3/3's square-1 = 22.5 days.

Sharad said: (Jul 15, 2015)  
Given A is thrice as good as B,

Therefore 3:1.

i.e 3x:x (ability to work). (Time taken is inverse of work).

Time taken by A and B to complete work = x:3x.

Difference A-B = 60.

Therefore x-3x = 60.

x = 60/2 = 30.

Now x:3x = 30:3(30).

= 30:90.

(A+B) 's 1 day = (1/30)+(1/90).

1 day = 2/45 work.

45/2 day = 1 work.

22. 5 day = 1 work.

Malleswari said: (Jul 20, 2015)  
A is thrice as good as B means 3A = B.

A finish the work 60 days less than B means A = B-60.

So, 3(B-60) = B.

3B-180=B.
2B=180.
B=90.

Then,

3A=B.
3A=90.
A=30.

So, A's I day work is 1/30.
B one day work is 1/90.

Then (A+B) 1 day work together is (1/30+1/90) = 2/45.

Total days they work together is. 45/2 = 22.5.

Manju Gouda said: (Jul 21, 2015)  
Let us take B's work days be 'x'.

Then A's will be x/3.

Given difference is 60.

Therefore x-x/3 = 60 on solving x = 90.

Therefore B days = 90 & A = 30.

A&B together will be (90*30)/(90+30) = 22.5 days.

Lins said: (Jul 31, 2015)  
1:3 = x:(x+60).

1/3 = x/(x+60).

So x+60 = 3x.

60 = 2x.

Then x = 30.

Satyawan said: (Aug 13, 2015)  
The explanation given above is very difficult to understand please try to explain the concepts as simple as possible.

Naresh said: (Aug 14, 2015)  
1:3.

Total 4 parts.

90/4=22.5 (one part).

Here one part means A's work. Remaining 77.5 belongs to B.

Ravi Yadav said: (Aug 23, 2015)  
Let A takes x days and B takes y days to complete work. In one day A completed 1/x part of work and B 1/yth.

According to question 1/x = 3*1/y and y-x = 60.

By solving x=30 and y= 90.

So in one day both completed (1/x + 1/y) = 4/90.

They can do it in = 90/4 = 45/2.

Nil said: (Aug 25, 2015)  
A    1x
-- = --- (RATIO OF TIME)
B    3x

And difference is given 60 days.

3x-1x=60.

1x = 30 days for A.
3x = 90 days for B.

I don't remember but I think I have posted the another method up above long time before.

Rahul said: (Aug 25, 2015)  
Can we solve such questions by LCM method? Please help.

Ramesh said: (Sep 24, 2015)  
Time ratio between A and B is 1:3.

A/B = 1/3------ (1).

B takes thrice the time taken by A.

A-B = 60 from A = B+60--- (2).

BY substituting (2) in (1).

Then get time taken by B to finish work in 90 days.

From (1) you get time taken by A to finish work in 30 days.

A's 1 day work is = 1/30.

B's 1 day work is = 1/90.

(A+B) 1 day's work is = (1/30+1/90) = 2/45.

Then time taken by the A and B working together is 45/2.

Anshul said: (Oct 5, 2015)  
We can solve this question easily.

A:B = 1:3.

Difference is 60.

Hence ratio becomes:

A:B = 30:90 = 1:3.

Here we can see diff is 60.

So our answer will be 90*30/90+30 = 270/12.

= 90/4 = 45/2 = 22+1/2.

Salman said: (Nov 15, 2015)  
So much confusing answer given. This is basically ratio problem.

60 days less means you have to take ratio of time and solve the problem. A is thrice as better as B means. B takes thrice time compared to A.

i.e Ratio of time taken by A/B = 1/3.

If B takes x days then A takes x-60 days time to complete the work.

i.e Ratio of time taken by A/B = x-60/x.

Therefore 1/3 = x-60/x.

Solve to get x = 90 therefore B takes 90 days and A takes 30 days.

Daily Work of A = 1/30.

Daily Work of B = 1/90.

Adding work of A and B.

Daily work of A and B is 4/90.

So time taken for both A and B to complete the work is 90/4 = 221/2 days!

Simple as that!

Nilu said: (Dec 8, 2015)  
A is thrice good as B.

So, ratio of work done is 3:1 and A taken 60 days less as compare to B.

Let time taken by B is x so time taken by A is x-60.

So 3:1::x:x-60.

3x-180 = x. So 2x = 180 and x = 90.

Time taken by B = 90 days so time taken By A is 30 days.

A's one day work = 1/30 and B's one day work is 1/90.

Total work done by both A and B in one day = 1/30+1/90.

= 3+1/90 = 4/90 = 2/45 = 22.5 days.

Pratim Pal said: (Jan 6, 2016)  
Hi friend.

This is one of easiest problem.

Here given that the ratio of time taken of A and B to complete one work in individually is 1:3.

So let us take A can do this work in X days and that of B is 3X days.

According to conditions B took 60 days more than A.

3X-X = 60.

2*X = 60.

X = 30.

So time taken by B is 3*30 = 90 days and by A is 30 days.

When A&B together do this work. The required time is:

= 1/(1/30+1/90).

= 1/((3+1)/90).

= 45/2 days.

Sagar said: (Jan 7, 2016)  
Please tell me how is the difference of time is 60 days?

Sudip Purakait said: (Jan 19, 2016)  
Hi @Sagar.

It is mentioned in the question.

Mukunda Saini said: (Jan 27, 2016)  
A is thrice as good as B. So A = 3x and B = x.

A is 60 greater than B. So 3x-x = 60.

2x = 60.

x = 30.

A = 90 and B = 30.

1/90+1/30 = 45/2.

Answer: 22 1/2.

Sravan said: (Jan 30, 2016)  
Since it's mentioned that A completed 60 days less than B.

We have to know there less than rate. Since it given A is thrice as good as B.

That means it takes 1 day to A to do Bs 3 day work.

So now we can know that A can do in (3-1) = 2 days less than B.

That means A less than days for B days for 2 its 3.

Similarly for 60 less day we need to multiply 2 by 30 to get 60. Since we do on 2 (A) side we have to multiply on 3 (B) side then we get.

= 2x30 : 3x30.

We get = 60 (for A day's lesser than B) : 90 (we got B days) that means A work days = 90-60 = 30.

So 1/30 + 1/90= 0.0444 amount of work per 1 day.

For 1 piece of complete work 0.4444/0.4444 = 1/0.4444 days.

That 1 piece of work done for 22.5 days by A & B together.

Bhupinder said: (Feb 4, 2016)  
Good explanations thanks.

Vamshidhar said: (Feb 5, 2016)  
In the explanation, said that,

"If difference of time is 60 days, B takes (3/2*60) = 90 days.

My opinion is if A can complete work in 60 days then B should complete work in 3*60 = 180 days but not in 90 days.

Can anyone explain this part?

Ram said: (Feb 15, 2016)  
Guys, this is pretty simple.

Given A : B = 3 : 1, difference in time taken is 2.

Let us consider it as 2 parts.

Then it's also given that A can complete the work with 60 days gap to B. Hence we can equate these 2 parts to 60 days.

Therefore 2 parts = 60 days.

A's part is 1 parts = 30 days.

B's part is 3 parts = 90 days.

Rest you know.

Hope you intelligent guys understand :).

Bunny said: (Apr 1, 2016)  
How to do LCM?

Dipa said: (Apr 1, 2016)  
3x:1x

=> 3x - 1x = 60.
=> 2x = 60.
=> x = 30.
=> 3x = 90.

A+b together work = 90 * 30 / 90 + 3.

=> 2700 / 120 = 22.5 days.

Pari said: (Apr 18, 2016)  
Thanks for giving a different solution.

Guarav said: (Apr 19, 2016)  
A is thrice as good as B
i.e A:B = 3:1.

The ratio will be same.
Now let a number of days for B be x.
Thus, for A it becomes (x - 60)
Now equate 3/1 = x/(x-60)(ratio of days of B to the days of A).
3x - 180 = x.
x = 180/3.
x = 90.
No of days by B is 90.
Hence days of A will be 30.

Ramya said: (Jun 3, 2016)  
Thank you @Siva.

It's simple to learn.

Inzamamul Haq said: (Jun 4, 2016)  
Workman.

A : B.
3 : 1.

Time taken;

A : B.
1 : 3.

A) if B finish work in 30 days then, A can finish it in 10 days. Now the difference in a day is 20.

B) if B finish work in 60 days then, A can finish it in 20 days. Now the difference in a day is 40.

C) if B finish work in 90 days then, A can finish it in 30 days. Now the difference in a day is 60.

Given question. The difference is 60 days. Hence, condition c) satisfies.

A 1-day work is 1/30.

B 1-day work is 1/90.

A + B 1 day work is 1/30 + 1/90 = 4/90.

Days to complete the work is 90/4 => 22 1/2.

Mahesh said: (Jul 14, 2016)  
Let consider B can do work in n days.

1 days work of B = 1/n.
So, A = n - 60.

1 day work of A =1/ (n - 60).
As given A = 3b.
1/ (n - 60) = 3 * (1/n).
n = 90.
B can do work in 90 days.
So A can do in 30 days.
Both = (1/30) + (1/90).
= 22 (1/2).

Insane said: (Jul 26, 2016)  
Let A be X where as b = 3x.
So,
3x - x = 60.
x = 30.
a = 30, b = 90.

Together they can do the work in 22 (1/2) days.

Priya said: (Aug 1, 2016)  
Please say me any shortcut methods to solve this problem.

Anonymous said: (Sep 24, 2016)  
Hello friends,

I just want to clear out something and that is according to the formula given. Here the answer is not correct.

There has been a mistake and that is it is wrongly solved becomes as the question goes hereby,

1) A is thrice as good as B so the ratio would be like 3:1. But it has been mentioned as 1:3 which is wrong according to my perception.

So please make it correct or give the correct sort of explanation to prove me wrong.

Sscaspirant said: (Oct 21, 2016)  
Hi guys

Here is a trick to solve it.
If B = 1, A = 3,
Therefore efficiency is A : B = 3 : 1.
Now, 60 days less means the difference of their efficiency.
2 ---> 60
1 ---> 30
Now you got 30.
A = 3 * 30 = 90,
B = 1 * 30 = 30,

LCM = 90.
Which is total work and total days = total work/total efficiency.
T.D = 90/4 = 45/2 = 22 (1/2)days.

Vaishnavi said: (Nov 8, 2016)  
Thanks @Sheetal it is best trick.

Mohin Uddin Mizan said: (Nov 10, 2016)  
Let B takes X days to the work.

Then B's 1 day's work = 1/x and A's 1/3x.
ACQ, 1/x - 1/3x = 60, So, x = 1/90.

As the difference is 60, so A needed 90 - 60 = 30 days.
(A + B)'s 1 day's work = 1/90 + 1/30 = 2/45.
So, to do the total work they need 45/2 or 22(1/2).

Soniya said: (Dec 17, 2016)  
Let t1 &t2 are time taken by A and B.
w1 & w2 are work done by A and B.

Ratio of the time taken by A and B =1 : 3.

Then, A = x, B = 3x (x is some constant).
We know that t1 = t2 - 60 (A takes 60 days less than B).
t2 - t1 = 60
3x - x = 60 (t1 = x, t2 = 3x)
x = 30.
Then t1=30 and t2 = 90.
Total work done by A& B(W) = w1 + w2.
W =1/t1 + 1/t2.
= 1/30 + 1/90 = 2/45.
Then time taken by A&B to finish the work is 45/2days.

Dineshkumar said: (Dec 28, 2016)  
Your answer is clear @Sundar, Thanks.

Udhay said: (Dec 28, 2016)  
I can't understand it. Please someone help me.

Devendra Kumar said: (Dec 28, 2016)  
Please tell me the easiest solution of this problem. Like LCM method.

Hari said: (Dec 30, 2016)  
A:B = 3:1 efficiency.
Because, A is Thrice the work as B.
So, A complete the work 60 days before.
Then 2---60
1--30,

So to find total work we just take it as;
A = 3 * 30. B = 1 * 30.

Total work is 90(LCM IS 90).
So, W = ED,
D = 90/4
= 22.5.

Black said: (Jan 1, 2017)  
Ratio of time taken by A & B = 1 : 3.
Suppose B takes x days to finish the job.
Then A takes (x-60) days.
So, (x-60) : x = 1:3
x= 90.
So rest are same.

@Verma Ji said: (Jan 31, 2017)  
Hello Friends: this shortcut formula is better to solve these type question in less time.

Alternate Method: Since 'A' is 'm' times as efficient as 'B' & takes 'D' days less than 'B', then the time required to complete the job together is given by,

T = m * D/(m^2 " 1)

T = 3 * 60 / [(3)^2 - 1] = 180 / 8 = 22 1/2 days.

Hari. said: (Mar 17, 2017)  
Thanks @Sachin.

Suresh said: (Mar 17, 2017)  
A is 3 times more efficient than B,
A=3B
A do the work less than 60 days compared to B,
A-60=B.

So, we can write it as,
A = 3(A+60)
A = 3A+180
2A = 180
A = 90
90-60 = B
B = 30.

Jpv said: (Mar 21, 2017)  
Ratio of no days taken to do work by and b= x : 3x.

It's give that diff= 60.

ie 3x-x = 60,
ie x = 30.

No of days taken by B=90.
No of days taken by A=30.

ie total no of days taken when work is done together= 1/30 +1/60,
= 22 1/2.

Jay said: (Mar 21, 2017)  
LET:
A = 3B.
where:
A = 1/x and B = 1/(x+60)
so;
(1/x) = 3[ 1/(x+60) ]
X = 30.

1/A + 1/B = 1/T
1/30 + 1/(30+60) = 1/T
Then, T = 22.5 answer.

Sahil Husain said: (Mar 31, 2017)  
A=3B ----------(1)
A-60=B----------(2) from equation 1 & 2

3B-60 = B
B=30 and A = 90
(A+B)'S 1 day work =1\90+1\30 = 2\45,
So (A+B)'s work = 45\2 = 22 1\2.

Dipak said: (Apr 4, 2017)  
Guys. I'm giving simple approach.

3x - x = 60
x = 30
So respective days are 90 and 30.
Total days together = 30 * 90/120 = 22.5.

Dhruv said: (Apr 13, 2017)  
Hi, According to me, the solution is;

A= 3B + 60,
So ,
A + B = 0
3B + 60 + B = 0
B = -15.

How to get the correct answer? Please, anyone explain me.

Sambhav said: (May 4, 2017)  
Hi guys.

It is given that A is thrice efficient then B then the efficiency of A is 3x and that of Y is x. then no of days are For A is(60-y) and for B is y. Then total work done is constant then
3x*(60-y) = x * y.
Then y = 45.
Then total work done by A is 45 X.
And rate of work of A and B will be 3x and x and if they work together the rate will be 4X.
So no of days will be = 45/4.

Sasikumar said: (May 19, 2017)  
Thanks @Deepti.

Esrak Ahmed Kafi said: (May 30, 2017)  
Let B can do it in 3x days.
So, A can do it in X days.
According to Question,
3x-x = 60.
So, X = 30.
So, A can do it 30 days while B can do it in 90 days.
Now in (1/30+1/90) days A & B can together do the work.
=45/2 = 22.5 days.

Rakesh said: (Jun 13, 2017)  
How 3/2? Explain.

Sumanth said: (Jun 21, 2017)  
Thanks for your explanation @Indhu.

Nagesh said: (Aug 17, 2017)  
Thank you for all the given explanation.

Pramod Patel said: (Aug 29, 2017)  
I think the best and universal approach is this:

A can do the work in X days, B takes X+60 days for same work,
But (X+60)/X=3/1 as time taken by A and B is in 1:3 ratio,
Solving we get X=30,
A's one day work is 1/30,
B's one day work is 1/90,
combining their one day work we get 1/30+1/90=2/45,
total time taken by them is 45/2.

Haritha said: (Aug 31, 2017)  
It's a clear explanation.

Thank you @Sheetal.

Tiya said: (Sep 19, 2017)  
Please solve this question.

If the ratio of work efficiency of A and B is 3:2. If A and B together finish a work in 5 days in how much days B alone complete the work?

Bismi Maria Jose said: (Sep 22, 2017)  
It is said A is 3 time as good as B.
ie. A=3*B
Again given,
A is able to finish a job in 60 days less than B.

say, B takes x days to complete 1 work
therefore A takes x-60 days to complete 1 work(same work)
A's 1 day work=1/x-60
B's 1 day work=1/x.
Substituting;

Applying in formula,
A=3B
ie. 1/x-60=3/x
so,x=90
x-60=30
so we got the number of days A alone and B alone worked i.e 60 and 90
1 day work of (A+B)=1 / 60 + 1 / 90 = 2/45,
So,nobr of days (A+B) worked = 45/2,
Answer is option B.

Purusottam said: (Sep 27, 2017)  
The answer must be 45 days.

Let B does the work in x days.
Now let's think about A's efficiency.

As far as the question is concerned,
3*100/x =100/60.

So, x=180,
Efficiency of A+B=100/60+100/180,
= 20/9%.
So 20/9...........1
1..............9/20
100..........9/20*100 .
=45.

Purusottam said: (Sep 27, 2017)  
Yes, correct @Sugumaran.

Anupam Kumar said: (Oct 1, 2017)  
Let us understand this in a much simpler way.

Let the time taken by B to finish the work be X days.
Then according to the question Time is taken by the A is (X-60).
Work done by B in one day is (1/X),
Work done by A in one day is (1/X-60),

And we know that A is three times faster than B, So work done by A in one day is three times the work done by B in one day.

So 3*(1/X)=(1/X-60), 3X-180=X, X=90, Therefore B takes 90 days to complete the work hence A take 30 days to complete the work, therefore together they take 1/(1/30+1/90) days, which is equal to 45/2.

Thank you all.

Saikrishna said: (Oct 22, 2017)  
a b
x 3x

2x=60 so x=30

total work=3*30=90
Ans=90/4=22 1/2.

Rohi said: (Oct 26, 2017)  
Ratio of times taken by A and B = 1:3.

Means B will take 3 times which A will do in 1 time.
If difference of time is 2 days, B takes 3 days,
If the difference of time is 10 days, B takes (3/2) * 10 =15 days.

Biplab Sarkar said: (Oct 30, 2017)  
Here given k=3, n=60.

So formula is -> kn/ (k^2-1) =3*60/ (3^2-1) =180/8=22 1/2 days.

Shaman said: (Oct 30, 2017)  
Please provide the solution of if A is 5 times better than B together they complete the work in 50 min then B alone can do the work in how many minutes.

Jack said: (Oct 31, 2017)  
Can anyone explain me why the step 3/2*60 used. I couldn't get the logic of finding difference as 2.

Pramod Nepal said: (Nov 6, 2017)  
Let see @Shaman.

A finish work in x day and B can 5x day. Then we can do A+B= 1/x +1/5x.

We have A+B = 50,

50 = 5x/6 after sol x= 60 it means A can do in 60 min and B 300 min.

Nik said: (Nov 8, 2017)  
How 4/90 comes?

Rizwan said: (Dec 19, 2017)  
From where does this 4/90 comes? How 4?

Vishal said: (Dec 27, 2017)  
I have better solution.

A:B-3:1(rate).
A:B-1:3(days).

Diff of 2 between ratio of days which is equivalent to 60 and 2*30=60.
Hence 30 will be multiplied to 1 and 3.
And we get 30 and 90.
Together days taken= 30 * 90/30 + 90 = 22 1/2.

Dusu Opo said: (Jan 17, 2018)  
Why 60 days? Please explain.

Sherin said: (Jan 18, 2018)  
Thank you @Showry.

Jiban said: (Feb 10, 2018)  
Can it be in this way?

B will take 180 days more than A. Then calculate for 1 day.

Can anyone solve this?

Nurun Nobi Khokon said: (Jun 1, 2018)  
Let A take x days
So, B takes x+60 days

3x = x+60 (B took 3 times more, so to make the equation equal he have to multiply the days taken by A by 3).
or, 2x = 60,
or, x = 30 days.

A takes 30 days and b takes 30+60 or 90 days.,
Now, (A+B)'s 1 day's work = (1/30+1/90) or 4/90 or 2/45,
So, total days required to do the whole work, 45/2 or 22.5 days.

Kavitalodhi said: (Jun 7, 2018)  
In the question clearly, say that A takes 60 days less than B.

So A can do the work in B-60 days,
And time ratio of A:B = 1:3,
1/3=B-x/B =>B=90,A=30.

So, A and B can do the work together 1/30+1/90 =>2/45,
Mix fraction of 2/45 is 22 1/2.

Mohit said: (Jun 15, 2018)  
3 x 60/3^2-1 = 22 1/2.

Balaji said: (Jun 28, 2018)  
Capacities of A:B=3:1.
Time taken ratio of A:B=1:3.
Difference of ratio in time is 2 = 60 days => A takes 30 days and B takes 90 days => 90/4=22 1/2.

Balaji said: (Jun 28, 2018)  
Capacities of A:B=3:1.
Time taken ratio of A:B=1:3.
Difference of ratio in time is 2 = 60 days => A takes 30 days and B takes 90 days => 90/4=22 1/2.

Balaji said: (Jun 28, 2018)  
Capacities of A:B=3:1.
Time taken ratio of A:B=1:3.
Difference of ratio in time is 2 = 60 days => A takes 30 days and B takes 90 days => 90/4=22 1/2.

Balaji said: (Jun 28, 2018)  
Capacities of A:B=3:1.
Time taken ratio of A:B=1:3.
Difference of ratio in time is 2 = 60 days => A takes 30 days and B takes 90 days => 90/4=22 1/2.

Rajashekar said: (Aug 9, 2018)  
Shortcut of these type of problems:

A&B = Difference * 'n' times / n^2 - 1.
= 60*3/3^2-1
= 180/9-1.
= 180/8=22.5 or 22 1/2.

Vickma said: (Aug 11, 2018)  
Here A is thrice EFFICIENT than B.

A=1 B= 3
A takes 60days less than B to finish a work, This shows that if B takes to complete a work by "X" days. Then A will take X - 60 days to complete a piece of work.

We know that A=1.
B=3
A= X - 60
B= X (No.of day to complete a work).

Cross multiply: 3(X-60)=X => 3X-180=X,
-180=-2X => X= 90.

WORKING TOGETHER: A+B = 1/X-60 + 1/X.
We know that X = 90,
A+B = 1/90-60 + 1/90,
=1/30+1/90,
=(3+1)/90 => 4/90 => 2/ 45.

Therefore, A+B takes 45/2 days to complete a piece of work.
A+B = 22 1/2.

Swetha said: (Aug 25, 2018)  
Since A finishes the job in 60 days less, from (ii) we get: 3X - X = 60.

A=30 B=90,
A+B=1/30+1/90.
=2/45.

A and B together can do the work in 45/2=22 1/2.

Naidu said: (Sep 5, 2018)  
It is a good and clear method, Thanks @Prashant.

Om Prakash Reddy said: (Sep 27, 2018)  
NO RATIO'S.

A is thrice as good as B.
This implies that if B take '' T '' days to complete the work, then A takes just ''T/3" days for same amount of the work.

Now coming to the second point in the question, A takes 60 days less than what B takes.

T/3 = T - 60.

----> T=90, ao B takes 90 days alone which implies A takes 30 days alone to complete work.

If A and B work together then no.of days required would be (1 / (1/30)+(1/90) ) which results in 22.5days.

Parveez said: (Sep 27, 2018)  
A is thrice as good as workman as B so the ratio of time taken by A and B is = 1:3.
Let, A completed the work in x days.
B completed the work in 3x days.

A's 1-day work= 1/x and B's 1-day work= 1/3x,
So, A+B 's 1-day work= 1/x+1/3x,
=4/3x.

So, A+B completed the work in 3x/4 days.
Since,
A finishes a job in 60 days less than B.
therefore , 3x-x=60.
x=30.
therefore, Working together A+B completed the work in 3x/4 days.
= 3*30/4.
= 45/2.
= 22 1/2 days.

Shreya said: (Nov 13, 2018)  
@All.

This is the easiest & shortest!.

Let a be x whereas b = 3x.
So, 3x " x = 60. x = 30.
therefore a = 30, b = 90.
so when they work together-> 1/30+1/60 = 4/90 = 2/45.

Together they can do the work in 22 (1/2) days.

Swarani said: (Dec 16, 2018)  
Your explanation is easy, thanks @Showry.

Jeev said: (Mar 1, 2019)  
3A = B.

If 60 is less than b(then 60 is two times of a)
then A=30,
b = 3 * 30 = 90,
a+b=1/30+1/90,
3*1/90+1/90,
(3+1)/90.

Where 4/90(to get days upside down).
90/4 = 22(1/2) days.

Chacha said: (Mar 3, 2019)  
It's simply.
3a = b.

Manohar said: (Mar 20, 2019)  
A+B = 1/60 + 1/180.

A is three times more efficient than B.

(So that if a takes 60 days then B takes 180 days).
And therefore;
2(A+B) = 180/4 = 22 * 1/2.

Chawdharya said: (Mar 26, 2019)  
A : B
TIME 1/3 : 1.
DAYS X-60 : X.

X-60/X = 1/3,
X= 90,
X-60 = 30.
A work efficiency = 1/90,
B work efficiency = 1/30,
A+B work efficiency = 1/90+1/30,
= 2/45,
work efficiency = work/time.
work is constant,so time = 45/2.
= 22.5.

Ameer said: (Apr 1, 2019)  
Thank you, excellent explanation.

a = 3b --> (1).

a-b = 60.
3b-b = 60.

2b = 60.
b = 30.
If b = 30 then from 1a = 3 x 30 = 90.

Now,
= 1/30+1/90.
= 3+1/90.

= 4/90 = 2/45.
= 45/2 = 22.5 days.

Samanth Kumar said: (Apr 11, 2019)  
Let A=X ,B=X+60 (GIVEN A TAKES 60 DAYS LESS THAN B,I CONSIDERED B TAKES 60 MORE DAYS THAN A).

Now, LCM OF X,(X+60) = X*(X+60),
Efficiency of A=(X*(X+60)) / X = X+60,
Efficiency of B=(X*(X+60)) / (X+60) = X.

Total work of A&B = (X(X+60))/(X+X+60),
We have A=3B (GIVEN).
X = 3(X+60),
X = 30.

Put in the equation and get the answer 45/2 =22(1/2).

Priya said: (May 16, 2019)  
The solution is;

A = x ,
B = 3x
x = 3x-60
x = 30
A = 30; B = 90;
1/30 + 1/90 = 2/45 = 22.5 days.

Harsh said: (May 25, 2019)  
I am not understanding anything this, please explain.

Anitha said: (Jun 8, 2019)  
A:B = 1:3
2p = 60
P = 30
30 : 90
1/30 + 1/90 = 2/45 = 22.5.

Sai said: (Jun 23, 2019)  
A is thrice as B, A:B=1:3.

B takes 60 days more than A to complete the work.

Lets consider A to complete the work in x days, therefore, B completes the same work in (x+60) days, x:(x+60).

Therefore,
As these are equally related to one and other;
1:3::x:(x+60).
Cross multiply we get x=30 days ie A can finish the work in 30 days,
Therefore B can do it in 90 days ie 3 times more days given.
Therefore:
(1÷30)+(1÷90).
= 22.5 days.

Tachime Sangma said: (Jul 4, 2019)  
How come 4/90? I don't understand.

Meg said: (Jul 21, 2019)  
First thing, the work done is always same, i.e. Work done by A = work done by B = work done by A+B.

So, if A does a work in x days then B does it in 60-x days.

Now, we can write A=3B

So, work done by A will be = 1*x = x
Work done by B will be = 3*(60-x)

As we know work done remains same then

x = (60-x)*3.
x = 45,

So, A's total time = 45.
B's total time = 60-x = 60-45 = 15.

So, now we can find the total time taken by A+B to complete the work as,
1/15 + 1/45 = 4/45.

It's one day work of A+B so reciprocal it to get the total time taken by them.
45/4 = 22.5 days

Subhendu said: (Aug 22, 2019)  
(3-1)=2------>60
1------>30
3------->90.

1's day work for A= 1/30
1's day work for b=1/90
Both 1's day work=(1/30+1/90)
= 4/90.

Total day = 90/4.
= 22(1/2).
The answer is B.

Neena said: (Aug 25, 2019)  
We can simplify it.

Assume if B worked for 90 days and
C worked for 30 days.

B's 1-day work = 1/90.
A's 1-day work = 1/30.

A+B = 4/90 work.
ie, 90/4 = 22.5.

Yash said: (Sep 23, 2019)  
(T*T.D)/(T^2-1).

T-EFFICIENCY.
T.D-TIME DIFFERENCE.

So;
3*60/9-1 = 22.5.

Yaswanth said: (Sep 23, 2019)  
Let's assume A completes its work in x days.

B completes in 3x days . since A is times efficient than B.
now, their difference is 60 days.
then, x-3x=60,
2x=60,
x=30,
A=30,B=90.

So, one days work of A and B together is A+B=1/30+1/90.
=4/90,
=2/45,
So one day work of A and B together is 2/45.
So A and B can complete the work in 45/2 days.
this equals to 22(1/2).

Sanishk said: (Oct 15, 2019)  
What is wrong with the below step?

A's 1-day work = 1/y.
Then, B's 1-day work = 1/3y.

Now,
A completes work before 60 days compared to B.

So,

1/y - 1/3y = 1/60
2/3y = 1/60
y = 40.

i.e., A completes in 40 days and B completes in 120 days,

Now, working together they complete in
1/A + 1/B = 1/40+ 1/120 = 1/30.

So, Together they complete in 30 days.

Rohan said: (Oct 16, 2019)  
A and B
Work 3:1
Time 1:3
i.e. 30:90 ......multiply by 30.

And also they have given that the difference between the time taken to complete the work is 60.

Hence when A and B time to work together,
1/30+ 1/90 = 2/45,

Defer for A and B to complete the entire work they require 45/2 which is equivalent to 22 and A half-day.

Aravind said: (Nov 19, 2019)  
Hi, friends, it's a bit tricky.

First, they found the time difference to do work between a and b.
Because the data we have is time difference in qn for 60 days consider.

Then. If a takes 1 day. B takes 3 days. So.

For 2 days time difference : 3 days for b

Then multiply both sides by 30 since the time difference is given

For 60 days time difference: 90 days of b.

I hope you all get it.

Then use ratio. A takes 30 days to complete work.

Dinesh said: (Dec 3, 2019)  
Please tell how A is working 30 days. How we calculate I don't understand.

Priti said: (Dec 11, 2019)  
***shortcut method******
D= no of days.
n= n times as fast.
D*n/n^2-1
60*3/3^2-1
180/9-1
180/8=90/4=22 1/2.

Abhijith said: (Dec 24, 2019)  
Can someone provide a solution for this problem using percentages or the efficiency ration ?

Mosa said: (Jan 20, 2020)  
Let a did this work in X days.
B can do it in 3x days.


X+60=3x.
X=30.

It means A can complete this work in 30 days and B in 90 days;
Capacity of;
A is 3.
B is 4.
A+B= 4.

TIME =90/4.

Rajesh said: (Apr 1, 2020)  
Work=3:1.
Time 1:3.
2 part=60 (difference).
1 part=30.

1*30:3*30=30:90.

He asked work of B( 90)can do by both in how many days.
90/(1+3)= 90/4=22.5 days.

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