# A and B can complete a certain work in 6 days and 8 days, respectively. They worked together for 3 days. C alone completed the remaining work in 2 day

156 views
in Aptitude
closed
A and B can complete a certain work in 6 days and 8 days, respectively. They worked together for 3 days. C alone completed the remaining work in 2 days. B and C together can complete $\frac{3}{4}$ of the same work in:
1. 6 days
2. 4 days
3. 3 days
4. 2 days

by (111k points)
selected

Correct Answer - Option 2 : 4 days

Given:

Time taken to complete the work by A = 6 days

Time taken to complete the work by B = 8 days

Formula used:

Total work = Efficiency × Time

Calculation:

LCM of 6 and 8 = 24 units = Total work

Efficiency of A = 24/6 = 4 units/day

Efficiency of B = 24/8 = 3 units/day

Work done by A and B together for 3 days = (3 × 7) = 21 units

Remaining work = (24 – 21) units = 3 units

Efficiency of C = 3/2 units = 1.5 units/day

3/4 of the total work = (3/4) × 24 units

⇒ 18 units

Required time taken by B and C = 18 ÷ (3 + 1.5)

⇒ 4 days

∴ Required time taken is 4 days