P and Q can complete a job in 24 days working together. P can alone complete it in 32 days. Both of them worked together for 8 days and then P left. The number of days Q will take to complete the remaining job is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 64 days
Work done by P and Q together in 1 day = 1⁄24
Work done by P alone in 1 day = 1⁄32
Work done by Q alone in 1 day = 1⁄24 − 1⁄32
= (4 − 3) ⁄ 96
= 1⁄96
Work done by P and Q in 8 days = 8 × 1⁄24
= 1⁄3
Remaining work = 1 − 1⁄3
= 2⁄3
Time taken by Q to complete remaining work = (2⁄3) ÷ (1⁄96)
= (2⁄3) × 96
= 64 days