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 ?

According to the question, 20 men + 30 boys = 24 men + 16 boys ∴ 4 men = 14 boys ∴ 2 men = 7 boys ∴ 2 men + 1 boy = 8 boys 2 men + 3 boys = 10 boys $herefore mathrm{M}_{1} mathrm{D}_{1}=mathrm{M}_{2} mathrm{D}_{2}$ $Rightarrow 10 imes 10=8 imes mathrm{D}_{2}$ $Rightarrow mathrm{D}_{2}=frac{10 imes 10}{8}=frac{25}{2}=12 frac{1}{2}$ days Alternative: Total work done by 2 men & 3 boys = 10 (2M + 3B) (∴ Total work = Efficiency × Time) According to the question 10 (2M + 3B) = 8 (3M + 2B) 20M + 30B = 24 M + 16B 14B = 4M Time taken to complete the work by 2 men & 1 boy

$=frac{10(2 mathrm{M}+3 mathrm{~B})}{2 mathrm{M}+mathrm{B}}=frac{10(2 imes 7+3 imes 2)}{2 imes 7+2}$

$=frac{25}{2}=12 frac{1}{2}$ days