2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days. In how many days can 2 men and 1 boy do the work?
Answer: C
Let 1 man's 1 day's work be 'm' and 1 boy's 1 day's work be 'b'. From the problem, \(10(2m+3b)=1\) and \(8(3m+2b)=1\). So, \(20m+30b=24m+16b \Rightarrow 4m=14b \Rightarrow m=3.5b\). Substitute this in the first equation: \(2(3.5b)+3b = 1/10 \Rightarrow 7b+3b=1/10 \Rightarrow 10b=1/10 \Rightarrow b=1/100\). Then \(m=3.5/100 = 7/200\). We need to find the time for 2 men and 1 boy. Their combined work per day is \(2m+1b = 2(7/200) + 1/100 = 14/200 + 2/200 = 16/200 = 2/25\). So, they will take 25/2 = 12.5 days.