A can complete one-third of the work in 10 days and B can do (3/5)th of the same work in 24 days. They worked together for 10 days. The remaining work was completed by C alone in 15 days. In how many days can C alone do (2/3)rd of the same work?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 24
A can complete one-third of the work in 10 days and B can do (3/5)th of the same work in 24 days.
So, A's 1-day work = 1/30
B's 1-day work = (3/5)/24 = 1/40
They worked together for 10 days. The remaining work was completed by C alone in 15 days.
⇒ (1/30 + 1/40) × 10 + 15 × (1/x) = 1
⇒ 1/x = 1/36
⇒ x = 36 = C alone can do the same work in x days.
So, C can complete the work in 36 days.
C alone do (2/3)rd of the same work in = 36 × 2/3 = 24 days