Two men undertake to do a piece of work for Rs. 1400. The first man alone can do this work in 7 days while the second man alone can do this work in 8 days. If they working together complete this work in 3 days with the help of a boy, how should the money be divided ?

Solution(By Examveda Team)

$$\eqalign{ & {\text{Boy's 1 day's work}} \cr & = \frac{1}{3} - \left( {\frac{1}{7} + \frac{1}{8}} \right) \cr & = \left( {\frac{1}{3} - \frac{{15}}{{56}}} \right) \cr & = \frac{{11}}{{168}} \cr} $$
∴ Ratio of wages of the first man, second man and boy
$$\eqalign{ & = \frac{1}{7}:\frac{1}{8}:\frac{{11}}{{168}} \cr & = 24:21:11 \cr & {\text{First man's share}} \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{24}}{{56}} \times 1400} \right) \cr & = {\text{Rs}}{\text{.600}} \cr & {\text{Second man's share}} \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{21}}{{56}} \times 1400} \right) \cr & = {\text{Rs}}{\text{.525}} \cr & {\text{Boy's man's share}} \cr & = {\text{Rs}}{\text{.}}\left[ {1400 - \left( {600 + 525} \right)} \right] \cr & = {\text{Rs}}{\text{.275}} \cr} $$