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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