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:

64 days

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