A and B can do a piece of work in 21 and 24 days respectively. They start the work together and after some days A leaves the work and B completes the remaining work in 9 days. After how many days did A leave?
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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