Question

Arpit has some marbles in his bag .He puts half of the marbles in a jar and one-sixth in his pocket . If total marbles are 10 more than twice of the remaining marbles in the bag, then find the number of marbles in the jar.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{arpit}\mathrm{has}\mathrm{x}\mathrm{marbles}\mathrm{in}\mathrm{his}\mathrm{bag}, \\ \mathrm{Number}\mathrm{of}\mathrm{marbles}\mathrm{in}\mathrm{jar}=\frac{\mathrm{x}}{2} \\ \mathrm{number}\mathrm{of}\mathrm{marbles}\mathrm{in}\mathrm{his}\mathrm{pocket}=\frac{\mathrm{x}}{6} \\ \mathrm{So}\mathrm{remaining}\mathrm{marbles}=\mathrm{x}-\frac{\mathrm{x}}{2}-\frac{\mathrm{x}}{6}=\frac{12\mathrm{x}-6\mathrm{x}-2\mathrm{x}}{12}=\frac{4\mathrm{x}}{12}=\frac{\mathrm{x}}{3} \\ \mathrm{Now}\mathrm{according}\mathrm{to}\mathrm{the}\mathrm{condition}, \\ \mathrm{x}=2\times \frac{\mathrm{x}}{3}+10 \\ \mathrm{x}=\frac{2\mathrm{x}}{3}+10 \\ 3\mathrm{x}=2\mathrm{x}+30 \\ 3\mathrm{x}-2\mathrm{x}=30 \\ \mathrm{x}=30 \\ \mathrm{So}\mathrm{number}\mathrm{of}\mathrm{marbles}\mathrm{in}\mathrm{the}\mathrm{jar}=\frac{\mathrm{x}}{2}=15 \end{gathered}$$