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**