Question : A and B can do a piece of work in 25 days. B alone can do $66 \frac{2}{3}$% of the same work in 30 days. In how many days can A alone do $\frac{4}{15}$th part of the same work?
Option 1: 18
Option 2: 15
Option 3: 12
Option 4: 20
Correct Answer: 15
Solution :
Days taken by A and B together to do total work = 25 days
Days taken by B to do = $66\frac{2}{3}$% of total work = 30 days
We know,
Number of days taken = $\frac{(\text{Total work})}{(\text{Efficiency})}$
Days taken by B to do $66\frac{2}{3}\%$ i.e. $\frac{2}{3}$rd of total work = 30
⇒ Days taken by B to do total work = $30 × \frac{3}{2}$ = 45 days
Let the total work be LCM of 25 and 45 = 225 units
The efficiency of A and B together = $\frac{225}{25}$ = 9
The efficiency of B = $\frac{225}{45}$ = 5
The efficiency of A = 9 – 5 = 4
Days taken by A to do $\frac{4}{15}$ part of total work = $(\frac{225}{4}) × (\frac{4}{15})$ = 15 days
Hence, the correct answer is 15 days.
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