Question

A and B undertook to do a piece of work for Rs. 4500. 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 the money is:
1. Rs. 2250
2. Rs. 750
3. Rs. 1500
4. Rs. 375

Answer 1

Correct Answer - Option 2 : Rs. 750

Given:

A alone can do the work in 8 days.

B alone can do the work in 12 days.

Formula:

work = time × efficiency 

Calculations:  

LCM of (8, 12) = 24

Let the total work be 24

Efficiency of A = 24/8 = 3 

Efficiency of B = 24/12 = 2

With the assistance of C they finished the work in 4 days.

⇒ Efficiency of A, B and C is 24/4 = 6

⇒ A + B + C = 6

⇒ C = 6 – 2 – 3 = 1

Their efficiency ratio is  A : B : C = 3 : 2 : 1

⇒ Share of C = (1/6) × 4500 = 750

∴ Share of C is 750 Rs.