Question : 4 men’s work is equal to 6 women’s work and 4 women’s work is equal to 6 boy's work. A boy can finish the work in 60 days. In how many days can the work be finished by a man and a woman together?
Option 1: 16
Option 2: 24
Option 3: 20
Option 4: 12
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Correct Answer: 16
Solution :
Let the efficiency of a woman, a man, and a boy be w, m, and b, respectively.
According to the question,
4m = 6w and 4w = 6b
Let b = 4 units per day, then w = 6 units per day, and m = 9 units per day.
Now, total work = 4 × 60 = 240 units
One day work of 1 man and 1 woman = 9 + 6 = 15 units
So, the time taken by 1 man and 1 woman to complete the work = $\frac{240}{15}=16$ days
Hence, the correct answer is 16.
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