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A and B complete the piece of work in 56 days, B and C in 40 days and A and C in 35 days. Find the share of C in the total of Rs. 40000.Marks : 2Negative Marks : 0Answer here2000010000120008000

Question

A and B complete the piece of work in 56 days, B and C in 40 days and A and C in 35 days. Find the share of C in the total of Rs. 40000.Marks : 2Negative Marks : 0Answer here2000010000120008000

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Solution

First, we need to find the rates at which A, B, and C work.

  1. A and B can complete the work in 56 days, so their combined rate is 1/56 work/day.
  2. B and C can complete the work in 40 days, so their combined rate is 1/40 work/day.
  3. A and C can complete the work in 35 days, so their combined rate is 1/35 work/day.

Adding these three rates together gives us:

2*(A's rate + B's rate + C's rate) = 1/56 + 1/40 + 1/35.

Solving this equation gives us:

A's rate + B's rate + C's rate = 1/20 work/day.

Now, subtracting the rates of A and B, B and C, and A and C from this total rate will give us the individual rates of A, B, and C.

  1. A's rate = 1/20 - 1/40 = 1/40 work/day.
  2. B's rate = 1/20 - 1/56 = 7/280 work/day.
  3. C's rate = 1/20 - 1/35 = 3/140 work/day.

The total payment of Rs. 40000 should be divided according to the rates at which A, B, and C work.

So, C's share = (C's rate / total rate) * total payment = (3/140) / (1/20) * 40000 = Rs. 12000.

So, C's share of the total payment is Rs. 12000.

This problem has been solved

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