Multiple choice

12 men can complete a piece of work in 36 days. 18 women can complete the same piece of work in 60 days. 8 men and 20 women work together for 20 days. If only women were to complete the remaining piece of work in 4 days, how many women would be required? 12 आदमी एक काम को 36 दिनों में पूरा कर सकते हैं | 18 महिलाएं उसी काम को 60 दिनों में पूरा कर सकते हैं | 8 आदमी और 20 महिलायें 20 दिनों तक साथ में काम करते हैं | यदि केवल महिलायें शेष काम को 4 दिनों में पूरा करती हैं, कितनी महिलाओं की आवश्यकता होगी ?

  1. 70

  2. 66

  3. 40

  4. 28
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A Correct answer
Explanation

12 men in 36 days means 1 man does 1/(12×36) work per day. 18 women in 60 days means 1 woman does 1/(18×60) work per day. Work done by 8 men + 20 women in 20 days = 20×[8/432 + 20/1080] = 20×[0.0185 + 0.0185] = 20×0.037 = 0.74 work. Remaining work = 0.26. For women to complete 0.26 work in 4 days: W × (1/1080) × 4 = 0.26, so W = 0.26×1080/4 = 70 women. The key is finding individual work rates, then calculating remaining work.

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