Aptitude - Time and Work - Discussion

21. 

A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in:

[A]. 4 days
[B]. 6 days
[C]. 8 days
[D]. 12 days

Answer: Option B

Explanation:

Suppose A, B and C take x, x and x days respectively to finish the work.
2 3

Then, 1 + 2 + 3 = 1
x x x 2

6 = 1
x 2

x = 12.

So, B takes (12/2) = 6 days to finish the work.


Afua said: (Jun 14, 2010)  
Where's 6 coming from?

Ritanjali Natua said: (Jun 28, 2010)  
1/x+2/x+3/x=6/x

Meera said: (Sep 13, 2010)  
A+B+C's 1 days work is = 1/6.

Therefore 2'days work (A+B+C) is=1/6*2=3.

B can do the work alone (2*3) =6.

So B takes 6 days to finish the work.

Is it right method? please anyone tell me.

Srihari said: (Sep 21, 2010)  
Hi Meera,

It is not right method because A+B+C's 1 day work is only 1/2 not 1/6.

Ananth said: (Oct 1, 2010)  
How the total work equation became as (1/x)+(2/x)+(3/x)=1/2

Please explain.

Kumar said: (Oct 25, 2010)  
How the work equation became as (1/x)+(2/x)+(3/x)=1/2

Keyan said: (Nov 11, 2010)  
How to solve it in 1:2:3 basis?

Shridhar said: (Nov 26, 2010)  
As the ques. says,
time taken by A is twice that of B and thrice that of C,so
this means that

A=2*B=3*C ----(eq.1)
dividing the whole equation by lcm(1,2,3)=6,we get
A/6=B/3=C/2

Now
one third of the workdone of B is finished in 2 days
therefore complete workdone of B will be finished in 3*2=6 days.

Lordy said: (Dec 18, 2010)  
once c the question pls it is mentioned a is twice of b OR thrice of c then how can we divide x,x/2,x/3. if it is mentioned as and then we can decide right?

Thameem said: (Dec 22, 2010)  
here is another way of solving

given
a=2b
a=3c
a+b=1/2 (work from days)

use a's value in the equation

2b+b=1/2

then 3b=1/2
b=1/6

then b can done work alone in 6 days(days from work)

Student said: (Dec 23, 2010)  
Hi thameem, hw can we write a+b=1/2? since three members are working is it not a+b+c=1/2....

please explain

Nayana said: (May 31, 2011)  
Hi,
Can any one exaplain why they have taken x,x/2,x/3, because in the question they have given A takes twice as much as B that means two times more than B but they are dividing it.

Manasa said: (Jun 11, 2011)  
@nayana
GIVEN:
A=2B,A=3C
solution:
consider A can do work in X days
X=2B...B=X/2;X=2C...C=X/3;
B can complete work in X/2days,B's 1 day work is 2/X
C can complete work in X/3days,C's 1 day work is 3/X
A's 1 day work is 1/X.
(A+B+C) 1 days work is[(1/X)+(2/X)+(3/X)]=1/2
6/X=1/2
X=12
therefore b can do work in ;B=X/2=12/2=6 days

Mini said: (Jul 8, 2011)  
A takes twice much time them B i.e. 2A=B...(i)
A takes thrice much time thn C i.e. 3A=C...(ii)

It is given dat workin together they can finish in 2 days
so A+B+C=1/2
Now put B=2A AND C=3A in this equ...
A+B+C=1/2
A+2A+3A=1/2
6A=1/2
A=1/2*6=1/12
Now put the value of A in equ.(i)
.i.e B=2A
=2*1/12
=1/6
Therefore B takes 6 days to complete the work.

Divya said: (Jul 10, 2011)  
A=2B=3C

A+B+C=2 ----(EQ.1)

WRITING a and c in terms of b,

A=2B, C=2B/3
IN EQ.1,

2B+B+2B/3=2

3B+2B/3=2


(9B+2B)/3=2

9B+2B=2*3

11B=6

B=6/11

that means, out of 11 days, b alone completes 6 days of work.

Md Ali Umar said: (Aug 5, 2011)  
Hi Mini you are making equ. 2A=B & 3A=C, but so many people a making equ. A=2B & A=3C .

Which one s correct, but both one is getting same answer. I'm confussing in this prob. Pls any one describe it ?

Kiran said: (Nov 30, 2011)  
B=2A
C=3A
A+B+C=2days
A+2A+3A=2days
so,6A=2days
A only takes (6*2)=12 days
B=2A,so B only takes (12/2)=6days

Aashish said: (Dec 31, 2011)  
Can anyone please explain me how 1/x comes? Because, I formed the equation as x+x/2+x/3=2 and got the wrong answer :-(

Bhaskar said: (Feb 2, 2012)  
See this solution:
Suppose A's 1 day's work= x
then B's 1 day's work = 2x,(Since its efficiency is twice of A)
C's 1 day's work will be 3x.(Since its efficiency is thrice of A)

Now, their combined 1 day's work will be
x+2x+3x

their combined 2 day's work will be
2(x+2x+3x)=1
gives x=1/12.

Since B's 1 day work is 2x =2 *1/12 = 1/6
Hence total days taken by B to complete the same work will be = 6 .

Jayasree said: (Feb 6, 2012)  
@nayana

Let time taken by B be x

then b= x
a = 2x which is equal to 3c
i.e 2x = 3c
c = 2x/3

so a = 2x ; b = x ; c = 2x/3

Dividing each by 2 => x , x/2 , x/3.

Hope it is clear.

Mann Prajapati said: (Apr 2, 2012)  
Suppose C can complete work in 18 days then A and B can complete the work in 54 and 27 days respectively.
Now A's 1 day work is 1/54 and B's 1 day work is 1/27 and C's 1/18.
Together 1/54+1/27+1/18=1/9.
Work finishes by together in 9 days.
Now when work complete in 9 days B's days are 27 so when work complete in 2 days B's days=?

27*2/9=6 days.

Mariam said: (May 4, 2012)  
Hai guys, i think mini is correct. from the question we get if B works for 1 hr, A takes 2 hrs to complete the same work i.e.,2A=B

Mahesh Sarangapani said: (Aug 9, 2012)  
Suppose A, B and C take x, x/2, x/3 days respectively to finish the work.
work done per day by

A is 1/x
B is 1/(x/2)=2/x
C ix 1/(x/3)=3/x

And the work done by A, B and C together per day is 1/2 (since work is completed in 2 days)

So 1/x + 2/x + 3/x = 1/2
6/x = 1/2
x = 12.

Answer : 6

Faith said: (Mar 14, 2013)  
My thoughts:

Let the time for A to do the job be X.
Let the time for B to do the job be 2X (since A takes twice as much time as B).
Let the time for B to do the job be 3X (since A takes thrice as much time as C).

So it takes all three X+2X+3X = 1/2 (days to finish the job).
This gives 6x=1/2. Therefore x=3.

Therefore the time taken for B to do the work is 2X.
Which is 2*3=6 which is equal to 6days.

It takes 3X that is 3*3 for C to do the work.
Which is equal 9 days.

With the above, you would find out that indeed A takes twice as much time as B and thrice as much time as C.

I hope this would suffice.

Kotha Sravani said: (Jun 21, 2013)  
Hai friends,

Taking the values of A,B,C as x, x/2, x/3.

1/x + 2/x + 3/x = 1/2.
On calculating we get,

6/x = 1/2.
Therefore, x = 12;

On substituting X = 12 in main equation.

1/12 + 2/12+ 3/12 = 1/2.

Hence, the value of B = 1/6.

Ravi said: (Nov 2, 2013)  
Can anyone please explain me that how these x, x/2, x/3 become 1/x + 2/x + 3/x.

Here I don't get is we take 1 day's work of A as 1/x and after that it's taken 2/x + 3/x as B and C's 1 day work but actually after A's 1 day work B's & C's work should be taken as 1/x/2 and 1/x/3.

Which becomes x/2 and x/3 So finally it should look like 1/x + x/2 + x/3.

Apeksha said: (Dec 19, 2013)  
Why 12 is divided by 2 in last?

Krishman Varges said: (Dec 20, 2013)  
This can be solved using physics. Force=Power/time. A, B and C does the same amount of work, hence, force is a constant. The power of three differs. Hence 1/t=f/p where f is a constant and t=2. 1/2=1/x+2/x+3/x.

Brijesh said: (Jan 12, 2014)  
Lets assume that A completes the work in 'x' days.

B completes the same amount of work in 'x/2' days because A takes twice the time than B.

C completes the same amount of work in 'x/3' days because A takes thrice the time than C.

Now the work completed by A in one day is '1/x'.

Work completed by B in one day is '2/x'
Work completed by C in one day is '3/x'

All three together can complete the work in '2' days as given in the problem. So the work done by all three together in one day is '1/2'.

Hence the equation: '(1/x + 2/x + 3/x) = 1/2'.

Evaluating the above equation gives the value 'x=12' which is the number of days taken by A to complete the work.

As we know that number of days taken by B complete the work is 'x/2', we substitute the 'x' value.

Hence the evaluation '12/2' where 12 is the value of 'x'.

HENCE THE TIME REQUIRED BY B TO COMPLETE THE WORK IS 6 DAYS.

Subhas said: (Aug 10, 2014)  
A can complete 1 unit/day.
B can complete 2 unit/day.
C can complete 3 unit/day.

Total works complete together by all in 1 days = 6 unit/day.

So, they complete in two days = 6X2 = 12 units.
So B takes 12/2 = 6 days to complete.

Rohini said: (Oct 5, 2014)  
a=2b or a=3c.

=>b=a/2 , c=a/3.
Let us assume a=x.

Then,
a b c
x x/2 x/3

Therefore., (1/x + 2/x + 3/x) = 1/2.
6/x = 1/2.
x = 12.
B alone = x/2 = 12/2 = 6.

Kaviya said: (Jun 28, 2015)  
How to comes the 1/x+2/x+3/x?

Wangchuk Drukpa said: (Aug 5, 2015)  
Let C takes x days to complete the work, then:

A, B, C.

3x, 3/2 x and x.

Their respective 1 day's work.

1/3x, 3/2x, 1/x now this is equal to 1/2 (as A+B+C takes 2 days to complete the work, thus their 1 day's work would be half).

Then we get x=4. Now 3/2 of 4 is 6.

Khushwinder Pal said: (Aug 10, 2015)  
Another method.

Suppose C = X.

C = 2X then B = 3X, A = 6X.

Then B = 2X = 2*3 = 6 days.

If asked A = 6*3 = 18 days.

Vidivelli said: (Aug 11, 2015)  
Let us consider the time taken by B is 2x.

So the time taken by A is "twice of B" then A=4x.

Similarly if time taken by B is x/2, the time taken by A is (2*x/2) = x; the time taken by C is x/3.

So the time taken by A is thrice of C (3* x/3). Hence we get x+x/2+x/3.

Since we consider work for one day we take inverse 1/x+2/x+3/x = 1/2.

G Jogi Rao said: (Sep 30, 2015)  
Hi @Kiran.

If 6A = 2 then A = 3.

But you said it A = 12 give proper explanation?

Dipika said: (Oct 1, 2015)  
If C takes x days to complete a work A will take 3x days.

If B takes y days to complete a work A will take 2y days.

But 3x = 2y, so x = 2/3y.

As per ques, 1/2y+y+2/3y = 1/2.

Therefore y = 6.

B takes 6 days to complete the work.

Naseem Ahmad Saifi said: (Jan 6, 2016)  
As per given:

2A = B => A = B/2......(1).

3A = C......(2).

=> 3*B/2 = C......(2) (from 1st A = B/2).

(A+B+C)'s do the work in 2 days.

So (A+B+C)'s 1 day work is = 1/2.

Put the value of A and C from 1st and 2nd.

= (B/2+B+3*B/2) 's 1 day work = 1/2.

=> 6B/2, 1 day work = 1/2.

=> B's 1 day work = 1/2*2/6 = 1/6.

So B complete work in 6 days.

Punitsw said: (Jan 26, 2016)  
In simple words:

A:B:C = 1:2:3 (Total 6 equivalent to A).

Now A, B and C together complete work in 2 days (i.e in 12 man days of A). So if A, B or C do the work alone, the required days would be:

A = 12 days.
B = 6 days.
C = 4 days.

Mona said: (May 1, 2016)  
In simple way:

A =2B , A = 3C,So ratio will be = A : B : C = 1 : 2 : 3.
A = 1 unit/day
B = 2unit/day
C = 3unit/day

A + B + C = 6unit/day.

We don't know the total work in units.
So,
A + B + C = 2 Days
TOTAL WORK/DAYS = 6.
TOTAL WORK = 6 * 2 = 12 UNITS.

So,B = 12/2 = 6 Days.

Vandana said: (Jun 11, 2016)  
One query, please answer this question:

A, B and C together can finish a piece of work in 12 days, A and C together work twice as much as B, A and B together work thrice as much as C. In what time could each do it separately?

Makvana Disha said: (Jun 19, 2016)  
We are also doing this,

A's 1 day work = 1/x, B's 1 day work = 2/x, C's 1 day work = 3/x.

So, (A + B + C) 's one-day work:

= (1/x + 2/x + 3/x).
= (1/x + 5x/x ^ 2).
= 1/x + 5.
= 6x/x = 6 Each of three.

Rakib said: (Dec 9, 2016)  
Let A = 12 days(twice than B& thrice than C),
B = 6 days,
C = 4 days.

Working together: (12 * 1/2) = 6 days.

Am I Right?

Raj said: (Dec 28, 2016)  
2A = B.......eqn1.
3A = C.......eqn2.

A + B + C = 2days
A + 2A + C = 2days (from the eqn1),
A + 2A + 3A = 2days(from the run2),
6A = 2days ,
A = 2/6,
A = 1/3 days.

i.e A takes 3days to work.

We have B=2A.
B=2(3),
B=6.
That's B takes 6 days to complete.

Ravi U S said: (Jan 9, 2017)  
There are many methods to solve a problem. As I feel Subhas 's method was good, follow it. A can do 1 unit of work in 1 day.
B can do 2 unit of work in 1 day.
C can do 3 unit of work in 1 day.
Totally A+B+C's 1 day's work = 12 units of work.
To do 12 units of work B take 6 days.

Ashok Kumar said: (May 17, 2017)  
Here is the simple shortcut

Given 2A= B
Given 3A = C

A+B+C=1/2
A+B+3A =1/2 since C=3A
4A+B=1/2
4(B/2) + B =1/2 since 2A=B => A=B/2
6B/2 =1/2 on solve

So final B=1/6 i.e B can do the work alone in 6 days.

Nwbeen said: (May 28, 2017)  
Where did 1/2 come from?

Pushpendra said: (Jun 2, 2017)  
Yes, right @Ravi.

Your method of explanation is clear, Thanks @Subhas.

Raj said: (Jun 13, 2017)  
@Ravi.

Where you get 12 unit work in 1 days and how please explain it?

Loki said: (Jun 18, 2017)  
a+2a+3a = 2days.
6a = 2days,
a = 1/3(this is total),
3*2 = 6.

Rajan said: (Jul 5, 2017)  
Best Solution,

Let A take x days to complete the work, Therefore in one day he completes 1/x of the work
Thus B will complete the work in x/2 days, Therefore in one day B will complete twice of A's work, i.e 2*(1/x)................(i)

Similarly in one day C will complete thrice of A's work, i.e 3*(1/x)

Together they take 2 days to complete the work, Therefore in one day they complete 1/2 or 50% of the work,.

Thus (work done by A + work done by B + work done by C) in one day = 1/2 or 50%
1/x + 2/x + 3/x = 1/2,
(1+2+3)/x = 1/2,
6/x = 1/2,
x=12, i.e The days required by A to complete the work.
Therefore B will take = x/2 = 12/2 = 6 days......................from eq.(i).

Bharath Ece said: (Nov 23, 2017)  
Simple Method. But I explained Elaborate.

A is twice time as B => A=2B
A is thrice time as c => A=3C
therefore;

B =A/2
C= A/3
A= A, A=2* (A/2)
A taken as X
A, B, C X, X/2, X/3 Days Respectively;
Rule of Flip or Time to Work
1/x +2//x+3/x =1/2
6/x =1/2
x=12

Asking b Alone.
B= x/2
so 12/2
B =6 Days.

Manish said: (Jan 17, 2018)  
One day work of a,b&c=1/2
let a's one-day work=x , then b's one day work 2x & c work 3x
x+2x+3x=1/2
6x=1/2
x=1/12
b's one day work=2*1/12
=1/6

Therefore total work in 6 days.

Bulu said: (Apr 25, 2018)  
@Manish, @Kiran.

Thanks for explaining the solution.

Ajay said: (Jul 8, 2018)  
Time ratio of A,B,C=6:3:2.
Efficiency ratio=1:2:3.

It takes 2 days for all of them to complete the work. So, Total work=(1+2+3)*2=12.

Time taken by B=12/2 = 6days.
Time taken by A=12/1 = 12days.
Time taken by C=12/3 = 4days.

Jatinder said: (Aug 17, 2018)  
a---12 days .
b ----6 days.
c --- 4 days.
lcm of 12,6,4 = 12.

The work done in one day by
A- 1
B-2
C-3
then total work done by B in 6 days.
6 is the answer.

Aadhi said: (Sep 18, 2018)  
@Ajay.

How to find efficiency ratio?

Rexi said: (Apr 2, 2019)  
Simply, it is solved by;

A=2B ; A=3C.
A/2=B ; A/3=C ---> time,
2/A=B; 3/A=C ---> efficiency,
1/A+2/A+3/A = 1/2 ---> A+B+C=1/2.
A = 12,
B = 6,
C = 4.

Rajshekar said: (Jul 26, 2019)  
A x.
B 2x.
C 3x.

A+B+B = 1/2,
X+2x+3x = 1/2.
6x=1/2.
X=1/12.

So, be alone =2x = 2 * 1/12 = 1/6 = 6days.

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