Question : The ratio of time taken to complete a work by a man and a woman is 2 : 3. The man and the woman can complete the work together in 24 days. In how many days can the woman complete the work alone?
Option 1: 20 days
Option 2: 40 days
Option 3: 60 days
Option 4: 30 days
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Correct Answer: 60 days
Solution :
A man and a woman can complete the work together in 24 days.
Time = $\frac{\text{Work}}{\text{Efficiency}}$
Time is inversely proportional to efficiency.
⇒ Ratio of time taken = $2 : 3$
$\therefore$ Ratio of efficiencies = $3 : 2$
Total work = $(3 + 2)\times24=120$
$\therefore$ Time take by a woman = $\frac{120}{2}$ = 60 days
Hence, the correct answer is 60 days.
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