If 12 men and 16 boys can do a piece of work in 5 days; while 13 men and 24 boys can do it in 4 days, then the ratio of the daily work done by a man to that of a boy is: MCQ with Answer and Explanation
If 12 men and 16 boys can do a piece of work in 5 days; while 13 men and 24 boys can do it in 4 days, then the ratio of the daily work done by a man to that of a boy is:
A. 3 : 1
B. 2 : 1
C. 3 : 2
D. 5 : 4
Answer: Option B
Solution (By JKSSB Mock Tests)
Total work = 5 * (12M + 16B) = 4 * (13M + 24B) => 60M + 80B = 52M + 96B => 8M = 16B => M/B = 16/8 = 2/1. Thus, the ratio is 2 : 1.
A can finish a work in 15 days and B in 25 days. They start together but B leaves 5 days before the completion of the work. Find the total number of days taken to complete the work.
Explanation:
Total work = LCM(15, 25) = 75 units. Efficiency of A = 5, B = 3. Let total days be x. A works for x days, B works for (x - 5) days. 5x + 3(x - 5) = 75 => 8x - 15 = 75 => 8x = 90 => x = 90/8 = 11.25 days.
Two pipes A and B can fill a cistern in 12 minutes and 15 minutes respectively. There is also a waste pipe C. If all three pipes are opened together, the cistern is full in 20 minutes. How long will C take to empty the full cistern?
Explanation:
Total capacity = LCM(12, 15, 20) = 60 units. Efficiency of A = 5, B = 4. Combined efficiency of A+B+C = 3. Efficiency of C = 3 - (5 + 4) = -6. Thus, C empties 6 units/minute. Time taken by C to empty the full cistern = 60 / 6 = 10 minutes.
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