Question : A can do a piece of work in 10 days, while A and B together can complete it in $2 \frac{1}{2}$ days. How long will B alone take to complete the work?
Option 1: $\frac{3}{10}$ days
Option 2: $\frac{10}{3}$ days
Option 3: $3$ days
Option 4: $4$ days
Correct Answer: $\frac{10}{3}$ days
Solution :
Given: A can do a piece of work in 10 days, while A and B together can complete it in $2\frac{1}{2}$ days.
Let the total work = LCM of 10 and $2\frac{1}{2}$ i.e., $\frac{5}{2}$ = 10 units
Now, the efficiency of A = $\frac{10}{10}$ = 1
and the total efficiency of A and B = 10 ÷ $\frac{5}{2}$ = 4
So, the efficiency of B = (4 – 1) = 3
$\therefore$ B alone can complete the work in $\frac{10}{3}$ days.
Hence, the correct answer is $\frac{10}{3}$ days.
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