Question

A and B undertook to do a piece of work for Rs. 4,500. A alone could do it in 8 days and B alone in 12 days. With the assistance of C they finished the work in 4 days. Then C’s share of money is (in rupees)
1. 2,250
2. 1,500
3. 750
4. 375

Answer 1

Correct Answer - Option 3 : 750

Given:

Time taken by A to do the work = 8 days

Time taken by B to do the work = 12 days

Time taken by A, B and C together to do the work = 4 days

Calculation:

Let the total work be LCM (8, 12, 4).

LCM (8, 12, 4) = 24 unit

In one day A do = 24/8 unit

⇒ 3 unit

In one day B do = 24/12 unit

⇒ 2 unit

In one day A, B and C do = 24/4 unit

⇒ 6 unit

In one day only C do = 6 - (3 + 2)

⇒ 1 unit

The proportion of their shares = A's 1-day work : B's 1-day work : C's 1-day work

⇒ 3 : 2 : 1

According to the question,

Total share = 4500

⇒ 6 unit = 4500

⇒ 1 unit = 750

So, C's share  = Rs. 750

∴ The C’s share of the money is Rs. 750.