Bunuel wrote:
Three boys can do the same work as one woman. If a work is completed by 36 boys in 28 days working 9 h every day, how many women must be required to complete the same work in 7 days working 6 h every day?
(A) 36 women
(B) 48 women
(C) 54 women
(D) 66 women
(E) 72 women
Solution:
One can make good use of variation and proportionality for such questions in order to avoid lengthy calculations and thought process. The key to solving this question easily is to analyze each element individually and multiplying accordingly. We are told that 3 boys can do the same work as one woman. So a woman is thrice as efficient as one boy is.
Listing down what all we are given:
For boys: Number - 36, Working days - 28, Hours per day - 9
For women: Number - ?, Working days - 7, Hours per day - 6
We can compute the number of women as below:
Women = 36 * 9/6 * 28/7 * 1/3
= 72
To arrive at the above think comparatively for each element, separately. Number: we are given 36 boys, and we need to find the corresponding number of women. So a comparison is not possible. Hence, put 36 as the numerator.
Hours: When comparing each element, disregard the difference in efficiency between boys as woman as the efficiency difference is dealt with separately in the element Efficiency Ratio. Assume that one woman is as efficient as one boy. So think link this: Boys work 9 hours a day and women work 6 hours a day. The amount of work to be done being fixed, if the number of working hours is reduced, we will need more number of people to work in order to complete the work in the same amount of time as before. Since the number of work hours for women is 6 against 9 for boys, the number of women should increase. So the fraction should be 9/6.
Days: Thinking for days is the same as was for hours. The number of work days for women are fewer than that for boys. So proportionality dictates that the number of women should increase. Therefore, the fraction should be 28/7.
Efficiency ratio: This element balances the equation by putting in efficiency information. For this element think like this: 1 woman is as efficient as three boys. So we will need fewer women as compared to boys because with all the other elements being the same, one woman is as efficient as three boys. So the fraction for this element should be such that reduces the overall number. Hence the fraction for this element should be 1/3.
So the answer is E, 72.