Aptitude - Time and Work - Discussion

@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!

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.

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.

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.

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.

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.

Hi, friends.

We know that A capability to do work is 3 times of B,ok
Then the the ratio of Efficiency is A:B=3:1

And the ratio of time (days) is A:B=1:3 ...(The ratio get reverse because Efficiency and time are inversely proportional)

Now,
Time taken by A to complete work = (X) day &
Time taken by B to complete work = (X+60) day.

*We compare the ratio of time
(X/X+60)=(1/3) get X = 30 ----> (1).

From (1) we get A need 30 Days and B need 90 days
Now take lcm of (A day and B-day).

That is LCM of (30 & 90).

A & B need to complete 90 work.

So, the efficiency of A is (3 w/d) & B's efficiency (1w/d).
When they together (A+B) = work done is (4w/d).
So (90w/(4w/d)) = 22 1/2.

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).

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!

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.