Multiple choice

6 men can complete a piece of work in 12 days. 8 women can complete the same piece of work in 18 days whereas 18 children can complete the piece of work in 10 days. 4 men, 12 women and 20 children work together for 2 days. If only men were to complete the remaining work in 1 days how many men would be required totally?/ 6 पुरूष किसी कार्य को 12 दिन में पूरा कर सकता है। जबकि 8 औरतें उसी कार्य को 18 दिन में और 18 बच्चे इसी कार्य को 10 दिन में कर सकते हैं। यदि 4 पुरूष, 12 औरतें और 20 बच्चे इसी कार्य को एक साथ प्रारंभ करते और 2 दिन कर सकते हैं। यदि शेष कार्य को 1 दिन में पूरा करने के लिये केवल पुरूष आये तो कुल कितने पुरूष की आवश्यकता होगी?

  1. 72

  2. 36

  3. 18

  4. 24

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

1 man's 1 day work = 1/(6×12) = 1/72. 1 woman's 1 day work = 1/(8×18) = 1/144. 1 child's 1 day work = 1/(18×10) = 1/180. Combined work in 2 days: 4/72 + 12/144 + 20/180 = 4/72 + 12/144 + 20/180 = 1/18 + 1/12 + 1/9 = 2/36 + 3/36 + 4/36 = 9/36 = 1/4. Remaining work = 3/4. If x men complete 3/4 work in 1 day: x/72 = 3/4, so x = 72/4 × 3 = 18. But wait, let me recalculate: 4 men + 12 women + 20 children in 2 days = 2×(4/72 + 12/144 + 20/180) = 2×(1/18 + 1/12 + 1/9) = 2×(2/36 + 3/36 + 4/36) = 2×(9/36) = 1/2. Remaining = 1/2. x men in 1 day: x/72 = 1/2, x = 36. Options A, C, and D are incorrect.