A can do a piece of work in 10 days, B in 15 days. They work for 5 days. The rest of the work was finished by C in 2 days. If they get Rs. 1500 for the whole work, the daily wages of B and C are ?

Solution(By Examveda Team)

$$\eqalign{ & {\text{Part of the done by A}} \cr & = \left( {\frac{1}{{10}} \times 5} \right) \cr & = \frac{1}{2} \cr & {\text{Part of the done by B}} \cr & = \left( {\frac{1}{{15}} \times 5} \right) \cr & = \frac{1}{3} \cr & {\text{Part of the done by C}} \cr & = 1 - \left( {\frac{1}{2} + \frac{1}{3}} \right) \cr & = \frac{1}{6} \cr} $$
So, (A's share) : (B's share) : (C's share)
$$\eqalign{ & = \frac{1}{2}:\frac{1}{3}:\frac{1}{6} \cr & = 3:2:1 \cr & \therefore {\text{A's share}} \cr & = {\text{Rs}}{\text{.}}\left( {\frac{3}{6} \times 1500} \right) \cr & = {\text{Rs}}.750 \cr & {\text{B's share}} \cr & = {\text{Rs}}{\text{.}}\left( {\frac{2}{6} \times 1500} \right) \cr & = {\text{Rs}}.500 \cr & {\text{C's share}} \cr & = {\text{Rs}}{\text{.}}\left( {\frac{1}{6} \times 1500} \right) \cr & = {\text{Rs}}.250 \cr & {\text{A's daily wages}} \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{750}}{5}} \right) \cr & = {\text{Rs}}.150 \cr & {\text{B's daily wages}} \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{500}}{5}} \right) \cr & = {\text{Rs}}.100 \cr & {\text{C's daily wages}} \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{250}}{2}} \right) \cr & = {\text{Rs}}.125 \cr & \therefore {\text{Daily wages of B and C}} \cr & = {\text{Rs}}{\text{.}}\left( {100 + 125} \right) \cr & = {\text{Rs}}{\text{.225}} \cr} $$