Question

A can do a certain work in 15 days. B is 25% more efficient than A. Both worked together for 4 days. C alone completed the remaining work in 8 days. A, B and C together will complete the same work in ?
1. 5 days
2. \(4\frac{1}{2}\) days
3. \(6\frac{1}{2}\) days
4. 4 days

Answer 1

Correct Answer - Option 1 : 5 days

Given:

Work done by A = 15 days

B is 25% more efficient than A

A and B worked together = 4 days

C alone completed the remaining work = 8 days

Formula used:

Work done = Time × Efficiency

Calculation:

B is 25% more efficient than A

⇒ (15 × 100/125) 

⇒ 12 days

B can do the work on 12 days

Now,

 LCM of 15 and 12 is 60

A's 1 day work = 4 units

B's 1 day work = 5 units

Work done by A and B work together for 4 days = (4 + 5) × 4 = 36 work

 Work left  = 60 – 36 = 24 units

C can do the remaining work = 24/8 units = 3 units

Now, A, B and C completed the whole work = 60/(4 + 5 + 3)

⇒ 60/12 days

⇒ 5 days

∴ A, B and C completed the same work together in 5 days