If 9 men and 12 boys can do a work in 4 days and 4 men and 16 boys can do the same work in 6 days, how long will 6 men and 24 boys take to complete the same work? यदि 9 आदमी और 12 लड़के एक काम को 4 दिनों में कर सकते हैं तथा 4 आदमी और 16 लड़के इसी काम को 6 दिनों में कर सकते हैं, तो 6 आदमी और 24 लड़के इसी काम को कितने समय में करेंगे?

Let 1 man's 1 day work = m, 1 boy's 1 day work = b. From first condition: 36m + 48b = 1/4. From second: 24m + 96b = 1/6. Multiplying first by 2: 72m + 96b = 1/2. Subtracting second from this: 48m = 1/2 - 1/6 = 1/3, so m = 1/144. Substituting: 24(1/144) + 96b = 1/6, giving 96b = 1/6 - 1/6 = 0, so b = 0. This is incorrect. Let total work = 36 units. 9m + 12b = 9 units/day, 4m + 16b = 6 units/day. Subtracting: 5m - 4b = 3. Also: 36m + 48b = 36, 24m + 96b = 36. Subtracting: 12m - 48b = 0, so m = 4b. Then 5(4b) - 4b = 3, giving 16b = 3. 6m + 24b = 6(4b) + 24b = 48b. Time = 36/48b = 36/(48 × 3/16) = 36/9 = 4 days.