time and work

[coolhabhi]

To do a certain work B would take three times as long as A and C together. And C twice as long as A and B together. The the men complete the work together in 10 days. How long would each one of them take?

A) 22,40,35
B) 18,36,42
C) 24,40,30
D) 22,36,40

I need a simple solution. I did get the answer for this though after quite a while.

[GMATGuruNY]

To do a certain work B would take three times as long as A and C together. And C twice as long as A and B together. The the men complete the work together in 10 days. How long would each one of them take?

A) 22,40,35
B) 18,36,42
C) 24,40,30
D) 22,36,40

Let A = A's rate, B = B's rate, and C = C's rate.
TIME and RATE are RECIPROCALS:
Three times as long implies 1/3 as fast.
Twice as long implies 1/2 as fast.

B would take three times as long as A and C together.
Thus, B is 1/3 as fast as A and C together:
B = (1/3)(A+C)
3B = A+C.

C would take twice as long as A and B together.
Thus, C is 1/2 as fast as A and B together:
C = (1/2)(A+B)
2C = A+B.

Subtracting the second equation from the first, we get:
3B - 2C = (A+C) - (A+B)
4B = 3C
B:C = 3:4.

Since B and C's RATE RATIO = 3:4, their TIME RATIO = 4:3.
Implication:
For every 4 hours that B works, C works for 3 hours.
Of the answer choices, only C offers the required time ratio:
24, 40, 30.

The correct answer is C.

[ganeshrkamath]

To do a certain work B would take three times as long as A and C together. And C twice as long as A and B together. The the men complete the work together in 10 days. How long would each one of them take?

A) 22,40,35
B) 18,36,42
C) 24,40,30
D) 22,36,40

I need a simple solution. I did get the answer for this though after quite a while.

Rate at which A works = 1/a
Rate at which C works = 1/c
Rate at which B works = 1/b

1/b = 1/3 * (rate at which A and C work together)
1/b = 1/3 * (1/a + 1/c)
3/b = 1/a + 1/c_____________________(1)

1/c = 1/2 * (rate at which A and B work together)
1/c = 1/2 * (1/a + 1/b)
2/c = 1/a + 1/b_____________________(2)

1/a + 1/b + 1/c = 1/10
From (1)
3/b + 1/b = 1/10
b = 40

1/a + 1/b + 1/c = 1/10
From (2)
2/c + 1/c = 1/10
c = 30

Choose C

Cheers