Discussion
If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be:
Answer: A
Let 1 man's work = m, 1 boy's work = b. From the problem, \(10(6m+8b) = 2(26m+48b) \Rightarrow 60m+80b = 52m+96b \Rightarrow 8m=16b \Rightarrow m=2b\). Total work can be calculated from the first condition: \(10(6(2b)+8b) = 10(12b+8b) = 10(20b) = 200b\). We need time for 15 men and 20 boys. Their combined work rate is \(15m+20b = 15(2b)+20b = 30b+20b = 50b\). Time taken = Total work / Rate = 200b / 50b = 4 days.
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