Question

A can do a work in 18 days more than the time taken by A and B together. B can do the same work in 8 days more than the time taken by A and B together. They agree to work with C and complete the work in 10 days. Total payment = ₹18000. Find C's share.

• A. ₹500
• B. ₹2000
• C. ₹3000
• D. ₹4500

Hint:

First find combined work rate, then individual rates, and finally divide payment in proportion to work done.

Answer 1

The Correct Option is B

A can do a work in 18 days more than the time taken by A and B together. B can do the same work in 8 days more than the time taken by A and B together. Let the time taken by A and B together be x days. 

So, A can do the work in x + 18 days and B can do the work in x + 8 days.

The work done by A in one day = 1/(x + 18)

The work done by B in one day = 1/(x + 8)

The combined work done by A and B in one day = 1/x

Therefore, 1/(x + 18) + 1/(x + 8) = 1/x

By taking the LCM of the denominators and solving, we get:

x² - 10x - 144 = 0

Solving this quadratic equation using the quadratic formula, we find:

x = 18 and x = -8

The time cannot be negative, so x = 18, implying A and B together can complete the work in 18 days.

Now, they involve C and complete the work in 10 days:

The work done by A, B, and C in one day together = 1/10

Therefore, 1/18 + 1/c = 1/10

Solving for 1/c gives c = 9, meaning C can do the entire work independently in 90 days.

Now, to find C's share of the payment:

A, B, and C together in one day do (1/18 + 1/90) of the work.

Calculating this gives:

1/18 + 1/90 = 1/14.4

Therefore, C’s part in the work done = (1/90) / (1/14.4) = 1/5.6

Hence, C's share of the payment is (1/5.6) * ₹18000 = ₹2000.

Thus, C's share is ₹2000.