Question

A can finish 3/5th of a task in 6 days and B can finish 2/3th of the same task in 12 days. A and B worked together for 5 days. C alone completed the remaining task in 8 days. B and C, working together, will complete the same task in:

• A. 10
• B. 18
• C. 12
• D. 15

Answer 1

Answer:

C. 12

Solution: Given: A can finish 35/ of a task = 6 days B can finish 2/3 of the same task = 12 days A and B worked together = 5 days C alone completed the remaining task = 8 days Concept Used: If a man can do a work in t days then in 1 day he will do 1/t part of the work Calculation: A alone can finish task = 6 × (5/3) ⇒ 10 days B alone can finish task = 12 × (3/2) ⇒18 days ⇒ A and B worked for 5 days = (5/10) + (5/18) ⇒ (45 + 25) /90 = 70/90 ⇒ 7/9 ⇒ Remaining work = 1 - (7/9) ⇒ 20/90 = 2/9 2/9th of work completed by C = 8 days C alone can finish task = 8 × (9/2) = 36 days ⇒ B + C working together can do in 1 day = 1/18 + 1/36 ⇒ (2 + 1)/36 = 3/36 = 1/12 In one day B and C together can complete = 1/12 of the task B and C together can complete a task = 12 day ∴ The number of days taken to complete a task B and C together is 12