Question : P can finish a work in 18 days. When he had worked for 5 days, Q joined him. If both of them together completed the remaining work in $\frac{13}{5}$ days, then in how many days can Q alone finish $66 \frac{2}{3}\%$ of the same work?
Option 1: 5
Option 2: 4
Option 3: 2
Option 4: 3
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Correct Answer: 3
Solution :
Let the total work be 18 units.
So, the efficiency of P = $\frac{18}{18}$ = 1
Now, work done by P in 5 days = (1 × 5) = 5 units
The remaining work = (18 – 5) = 13 units
So, 13 units of work done by P and Q in $\frac{13}{5}$ days,
Now, the total efficiency of P and Q = $13\ ÷\ \frac{13}{5}$ = 5
So, the efficiency of Q = (5 – 1) = 4
Also, $66\frac{2}{3}\%$ of total work = $\frac{2}{3}$rd of the total work = $\frac{2}{3}$ × 18 = 12 units
So, the required days for Q alone to do the 12 units of work = $\frac{12}{4}$ = 3 days
Hence, the correct answer is 3.
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