Discussion

Explanation:

In 9 days, B will do 9/24 = 3/8th of the work.

Hence, A and B together did 1 – 3/8 = 5/8th of the work together.

Now, A and B can complete;

1/21 + 1/24 = 5/56th of the work in one day.

Hence, they will complete, 5/8th of the work in = 5/8 × 56/5 = 7 days.

Alternately,
Let the work to be done = LCM (21, 24) = 168 units

∴ Efficiency of A = 168/21 = 8 units/day, and
Efficiency of B = 168/24 = 7 units/day

Let A and B work together for x days after which B completes the remaining work in 9 days.

∴ Total work done = Work done by A and B in 4 days + Work done by B in x days

⇒ 168 = (8 + 7) × x + 7 × 9
⇒ 168 = 15x + 63
⇒ 105 = 15x
⇒ x = 7 days

∴ A leaves after 7 days.

Hence, option (b).

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