Question : A can do in one day three times the work done by B in one day. They together finish $\frac{2}{5}$th of the work in 9 days. The number of days by which B can do the work alone is:
Option 1: 90 days
Option 2: 120 days
Option 3: 100 days
Option 4: 30 days
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Correct Answer: 90 days
Solution :
Given: A can do in one day three times the work done by B in one day. They together finish $\frac{2}{5}$th of the work in 9 days.
Let the efficiency of B = $a$ units,
So, the efficiency of A = 3$a$ units
Here, $\frac{2}{5}$th of the work is done by them in 9 days.
So, the total work is done by them in (9 × $\frac{5}{2}$) = $\frac{45}{2}$ days
We know,
Total work = Total efficiency × Number of days = $(a+3a)×\frac{45}{2}$ = 90$a$ units
$\therefore$ The required days for B to do the work alone = $\frac{90a}{a}$ = 90 days
Hence, the correct answer is 90 days.
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