Working alone A can do a job in 24 days, while B will take 12 days. Working together, B and C, will take 8 days; working together A and D will take 16 days. If all four of them worked together and got Rs.9,000 for completing the task, what is D’s share of Rs.9000?

Explanation:

The amount of money to be distributed is proportional to the amount of work done.

In a day, A, B, C and D do work in the following ratio

A:B:C:D :: 1\24:1\12:(1\8−1\12):(1\16−1\24)

or A:B:C:D :: 1\24:1\12:1\24:1\48 …(1)

The share of revenue that each of them gets will be directly proportional to the amount of work done.

In a day, the four of them complete work in the ratio given in equation (1).

The ratio can be written as 48\24:48\12:48\24:48\48 (48 is the LCM of 24. 12 and 48) = 1 : 4 : 2 : 1

Now, if A gets 2x, then B will get 4x, C will get 2x and D will get x out of the total of 2x +

4x + 2x + x = 9x .

We know 9x = Rs.9000.

Hence, the amount that D gets i.e.. x = 1\9×9000 = Rs.1000