Question

A and B undertake to do a piece of work for Rs. 330. A can do it in 11 days and B can do it in 22 days. With the help of C, they finish it in 6 days. How much should C be paid for his work?

• A. Rs. 140
• B. Rs. 70
• C. Rs. 80
• D. Rs. 60

Answer 1

Answer:

D. Rs. 60

Solution: Given Total payment for work = Rs. 330 A can do it in 11 days B can do it in 22 days With the help of C, they finish it in 6 days Concept: The work done is inversely proportional to the time taken. The share of each person is proportional to the work done by them. Solution: ⇒ Work done by A in one day = 1/11 ⇒ Work done by B in one day = 1/22 ⇒ Work done by A, B, and C in one day = 1/6 ⇒ Therefore, work done by C in one day = 1/6 - (1/11 + 1/22) = 1/33 ⇒ So, the share of C = (Work done by C / total work done in one day) × total payment ⇒ = (1/33)/(1/6) × Rs. 330 = Rs. 60 Therefore, C should be paid Rs. 60 for his work. Shortcut Trick A = 11 days B = 22 days A + B + C = 6 days so Let the total work = LCM(11,22,6) = 66 Efficiency of A = 6 Efficiency of B = 3 Efficiency of A + B + C = 11 So Efficiency of C = 11 - 6 - 3 = 2 So C's share = (2/11) × 330 = Rs. 60