Question

A work can be completed by A, B and C in 12 days,15 days and 24 days respectively. A started the work and worked for 2 days then B joined A and together they worked for 5 days. C completed the remaining work alone. Find the time taken by C to complete remaining work. 
1. 1 days
2. 2 days
3. 5 days
4. 3 days

Answer 1

Correct Answer - Option 2 : 2 days

Given:

A, B and C can complete a work in 12 days,15 days and 24 days respectively.

Formula used:

Total work = Efficiency × Time

Calculation:

Let total work be 1 unit

Work done by A in 2 days = 2/12 unit

Work done by (A + B) in 5 days = 5 × {(1/12) + (1/15)} unit

⇒ 5 × 9/60 unit

⇒ 9/12 unit

So, remaining work = 1 - {(2/12) + (9/12)} unit

⇒ 1- (11/12) unit

⇒ 1/12 unit

So, time taken by C to complete 1/12 work = (1/12)/(1/24) days

⇒ 24/12 days

⇒ 2 days

∴ C complete remaining work in 2 days.