A can do a certain job in 25 days which B alone can do

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A can do a certain job in 25 days which B alone can do in 20 days. A started the work and was joined by B after 10 days. The work lasted for ?

1. 12¹/₂
2. 14²/₉
3. 15 days
4. 16²/₃

Correct Option: D

A's 10 day's work = 10 x (1/25) = 2/5
Remaining work = 1 - 2/5 = 3/5
Work was done by (A + B) in 1 day = (1/25 + 1/20) = 9/100
∴ 3/5 work was done by (A + B) in (100/9 x 3/5) = 20/3 days

Hence, the work lasted for (10 + 6²/₃) = 16²/₃ days.