Question : A can do a piece of work in 30 days while B can do it in 40 days. How many days can A and B when working together do it?
Option 1: $42\frac{3}{4}$ days
Option 2: $27\frac{1}{7}$ days
Option 3: $17\frac{1}{7}$ days
Option 4: $70$ days
Correct Answer: $17\frac{1}{7}$ days
Solution :
Given:
A can do a piece of work in 30 days while B can do it in 40 days.
(A + B)'s work in 1 day $=\frac{1}{30} + \frac{1}{40}=\frac{4+3}{120} = \frac{7}{120}$
$\therefore$ (A + B) can complete the work in $=\frac{120}{7} = 17\frac{1}{7}$ days
Hence, the correct answer is $17\frac{1}{7}$days.
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