coolhabhi wrote: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.
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