Question : $x$ does $\frac{1}{4}$ of a job in 6 days. $y$ completes the rest of the job in 12 days. Then $x$ and $y$ could complete the job together in:
Option 1: $9$ days
Option 2: $9\frac{3}{5}$ days
Option 3: $8\frac{1}{8}$ days
Option 4: $7\frac{1}{3}$ days
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Correct Answer: $9\frac{3}{5}$ days
Solution :
Time taken by $x$ to complete $\frac{1}{4}$ of a job = 6 days
Time taken by $x$ to complete whole work = 6 × 4 = 24 days
Part of work done by $x$ in a day = $\frac{1}{24}$
Time taken by $y$ to complete $\frac{3}{4}$ of a job = 12 days
Time taken by $y$ to complete whole work = $\frac{12 × 4}{3}$ = 16 days
Part of work done by $y$ in a day = $\frac{1}{16}$
Part of work done by $x$ and $y$ in a day = $\frac{1}{24}$ + $\frac{1}{16}$ = $\frac{4 + 6}{96}$ = $\frac{10}{96}$
Time taken by $x$ and $y$ together to complete whole work = $\frac{96}{10}$ = $9\frac{3}{5}$ days
Hence, the correct answer is $9\frac{3}{5}$ days.
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