10 children can complete a piece of work in 240 days .18 Men can complete the same piece of work in 72 days. And 15 women can complete it in 180 days. In how many days can 9 Men,30 women and 10 children together complete the piece of work? 10 बच्चे किसी कार्य को 240 दिन में पूरा कर सकते है। 18 आदमी उसी कार्य को 72 दिन में 15 औरतें 180 दिन मे पूरा कर सकती है। यदि 9 आदमी 30 औरतें और 10 बच्चे साथ-साथ इस कार्य को कितने दिनों में कर लेगें?

First calculate the total work in terms of each group's capacity: 10 children × 240 days = 2400 child-days of work; 18 men × 72 days = 1296 man-days; 15 women × 180 days = 2700 woman-days. The per-day rate for one child is 1/2400, one man is 1/1296, one woman is 1/2700. The combined rate of 9 men + 30 women + 10 children = 9/1296 + 30/2700 + 10/2400. Simplifying: 9/1296 = 1/144 ≈ 0.00694; 30/2700 = 1/90 ≈ 0.01111; 10/2400 = 1/240 ≈ 0.00417. Sum = 0.02222 work per day. Days = 1 ÷ 0.02222 = 45 days.