Question

divide Rs.7100 between A and B such that one-fifth of A's share exceeds one- sixth of B's share by Rs.155.

Answer 1

Dear student,

$$\begin{gathered} LetA\text{'}ssharebeRsxandB\text{'}ssharebeRs(7100-x) \\ \frac{1}{5}A\text{'}sshare-\frac{1}{6}B\text{'}sshare=155 \\ \frac{1}{5}x-\frac{1}{6}(7100-x)=155\Rightarrow \frac{x}{5}+\frac{x}{6}-\frac{7100}{6}=155 \\ \frac{11x-35500}{30}=155\Rightarrow 11x-35500=4650\Rightarrow 11x=4650+35500=40,150 \\ x=\frac{40,150}{30}=1,338.34 \\ A\text{'}sshare=Rs1,338.34andB\text{'}sshare=7100-1338.34=5,761.66 \end{gathered}$$
Regards