Ram and Sham Money Problem Breakdown

This problem involves calculating Ram's share of money based on the total amount he and Sham possess and a given fractional relationship between their money.

Ram and Sham Money Equations

Let $R$ represent the amount of money Ram has, and $S$ represent the amount of money Sham has.

• The total amount of money is ₹ 285: $R + S = 285 \quad (1)$
• The condition given is that $2/3^{rd}$ of Ram's money equals $3/5^{th}$ of Sham's money: $\frac{2}{3}R = \frac{3}{5}S \quad (2)$

Calculating Ram's Specific Share

We solve these two equations simultaneously to find the value of $R$ (Ram's money).

1. Express $S$ in terms of $R$: Rearrange equation (2) to find $S$: $S = \frac{2}{3}R \times \frac{5}{3}$ $S = \frac{10}{9}R$
2. Substitute $S$ into equation (1): Replace $S$ in the total money equation (1) with the expression derived above: $R + \frac{10}{9}R = 285$
3. Solve for $R$: Combine the terms involving $R$: $\frac{9R + 10R}{9} = 285$ $\frac{19R}{9} = 285$ Isolate $R$: $R = 285 \times \frac{9}{19}$ Perform the calculation ($285 \div 19 = 15$): $R = 15 \times 9$ $R = 135$

Therefore, the money with Ram is ₹135.