Question

A and B can do a piece of work in 10 days and 15 days, respectively. They work together for 4 days. The remaining work is completed by C alone in 12 days. C alone will complete \(\frac{4}{9}\) part of the original work in:
1. 24 days
2. 12 days
3. 20 days
4. 16 days

Answer 1

Correct Answer - Option 4 : 16 days

Given:

Time taken by A to complete the work is 10 days.

Time taken by B to complete the work is 15 days.

Time taken by C to complete remaining work is 12 days.

Concept Used:

Time taken = (Total work done)/(Efficiency)

Calculation:

Let the work done by A, B and C be in Units.

Total Work done by (A + B) = L.C.M of (10, 15) 

⇒ 30 Units

Now,

Efficiency of A = Total Work/Time taken

⇒ 30/10

⇒ 3 units per day

Efficiency of B = Total Work/Time taken

⇒ 30/15

⇒ 2 units per day

Total Work done by (A + B) in 4 days = (Sum of efficiency of A and B) × 4

⇒ (3 + 2) × 4

⇒ 20 units

Remaining Work = (30 - 20)

⇒ 10 units

Efficiency of C for completing remaining work = 10/12

⇒ (5/6) unit per day

Then,

Time taken by C to complete (4/9) part of original work = 30 × (4/9) × (6/5)

⇒ 16 days

∴ Time taken by C to complete (4/9) part of original work is 16 days.