Question : A can finish a work in 24 days and B in 30 days, individually. They work together for 11 days. The percentage of the work still to be finished will be:
Option 1: 18%
Option 2: 16%
Option 3: 17.5%
Option 4: 12.5%
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Correct Answer: 17.5%
Solution : Time taken by A alone to complete the work = 24 days ⇒ Part of work done by A alone in a day = $\frac{1}{24}$ Time taken by B alone to complete the work = 30 days ⇒ Part of work done by B alone in a day = $\frac{1}{30}$ Let the time taken by A and B together to complete the work = $x$ ⇒ Part of work done by A and B in a day = $\frac{1}{x}$ ⇒ $\frac{1}{24}$ + $\frac{1}{30}$ = $\frac{1}{x}$ ⇒ $\frac{5+4}{120}$ = $\frac{1}{x}$ ⇒ $x$ = $\frac{120}{9}$ = $\frac{40}{3}$ days Now, part of the work done by A and B in 11 days = $\frac{11}{\frac{40}{3}}$ = $\frac{33}{40}$ ⇒ Part of work left = $\frac{7}{40}$ ⇒ Percentage of work left = $\frac{7}{40}×100$ = 17.5% Hence, the correct answer is 17.5%.
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