Aptitude - Time and Work - Discussion

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.

Hi @Kiran.

If 6A = 2 then A = 3.

But you said it A = 12 give proper explanation?

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.

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.

Where did 1/2 come from?

Yes, right @Ravi.

Your method of explanation is clear, Thanks @Subhas.

@Ravi.

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

a+2a+3a = 2days.
6a = 2days,
a = 1/3(this is total),
3*2 = 6.

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).

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.