Question

Surbhi can do a piece of work in 24 days. She completed 3/8 of the work and then left it. Amit can complete the remaining work in 10 days. Working together, they will complete 125% of the same work in:

• A. 10
• B. 9
• C. 12
• D. 15

Answer 1

Answer:

C. 12

Solution: Given: Surbhi can do a piece of work in 24days Surbhi after completed (3/8)th work and then left The remaining work is completed by Amit in 10 days Calculation: Let the total work be x units Efficiency of Surbhi = x/24 = x/24 units/day According to question: (3/8) × x = 3x/8 units Surbhi after doing 3x/8 units left the work Remaining work = x – (3x/8) = 5x/8 units Amit done the remaining work in 10 days Efficiency of Amit = (5x/8) ÷ 10 = x/16 units/day 125% of the work = (125/100) × x = 5x/4 units Efficiency of surbhi and amit = (x/24) + (x/16) = 5x/48 units/day Time taken to complete 5x/4 work = (5x/4) ÷ (5x/48) days ⇒ 12 days ∴ Time taken to complete the 125% of the work together is 12 days Alternate Method Calculation: Let the total work be 72 units Efficiency of Surbhi = 72 / 24 = 3units/day According to question: (3/8) × 72 = 27units Surbhi after doing 27units left the work Remaining work = 72 – 27 = 45units Amit done the remaining work in 10days the efficiency of Amit = 45/10 = 4.5units/day 125% of the work = (125/100) × 72 = 90units Efficiency of Surbhi and Amit = (3 + 4.5) = 7.5units/day Time taken by Amit and Surbhi working together to complete 125% work = 90/7.5 days ⇒ 12 days ∴ The time taken to complete 125% of the work together is 12 days