Question

A and B can do a work in 15 days and 10 days respectively. They begin the work together but B leaves after two days. Now A completes the remaining work. The total number of days needed for the completion of the work is:

• A. 15 days
• B. 18 days
• C. 12 days
• D. 10 days

Answer 1

Answer:

C. 12 days

Solution: Given: A can-do work in 15 days B can do work in 10 days Concept used: A can do a work in n days So, A's one day work = 1/n Calculation: A can-do a work in 15 days ⇒ A's one-day work = 1/15 B can do a work in 10 days ⇒ B's one day work = 1/10 A and B's one day work = 1/15 + 1/10 ⇒ 5/30 = 1/6 Two days work of A and B will be 2/6 = 1/3 Remaining work after B left = 1- 1/3 = 2/3 A will finished remaining work in = (2/3) × 15 = 10 days ∴ Total number of days to complete work is 10 + 2 = 12 days Shortcut Trick LCM of 15 and 10 is 30 A = 15 × 2 = 30 B = 10 × 3 = 30 Total work = 30 unit B does 3 unit work in one day A does 2 unit work in one day ⇒ (A + B)'s one day's work is (3 + 2) unit = 5 unit ⇒ (A + B)'s two days' work is (5 × 2) unit = 10 unit ⇒ Remaining work = 30 - 10 = 20 unit A will complete remaining work in, 20/2 = 10 days Total number of days = (10 + 2) days = 12 days ∴ Total number of days to complete work is 12 days