Aptitude - Time and Work - Discussion

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.

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?

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.

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.

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).