Question

A can do 1/3 of a work in 30 days. B can do 2/5 of the same work in 24 days. They worked together for 20 days. C completed the remaining work in 8 days. Working together A, B and C will complete the same work in:

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

Answer 1

Answer:

C. 12 days

Given - A can do 1/3 of a work in 30 days B can do 2/5 of the same work in 24 days C completed remaining work in 8 days. Solution - ⇒ A can do 1/3 of a work in 30 day ⇒ A completed work in 90 days ⇒ B can do 2/5 of the same work in 24 days ⇒ B can completed work in 60 days. ⇒ Let the total work = LCM (90, 60) = 180 unit ⇒ Efficiency of A = 3 unit/day ⇒ Efficiency of B = 2 unit/day ⇒ They both worked for 20 days. work done in 20 days = 20 × 5 = 100 unit ⇒ remaining work = 180 - 100 = 80 unit ⇒ Remaining work done by C in 8 days, ⇒ Efficiency of C = 10 unit/day ⇒ Efficiency of (A + B + C) = 15 unit/day ⇒ Work completed = 180/15 = 12 days ∴ If all worked together, the work completed in 12 days.