Question

₹$6500$ were divided equally among a certain number of persons. There had been $15$ more persons , each would have got ₹ $30$ less, find the original number of persons.

Answer 1

Step-1: Make equation from given condition:

Let the original number of persons be $x$ .

Then, share of each person= ₹$\frac{6500}{x}$

When the number of person increased by $15$

Then, new share=₹ $\frac{6500}{x+15}$

Step-2: Solve for $\mathit{x}$:

According to question,

$$\begin{gathered} \frac{6500}{x}-\frac{6500}{x+15}=30 \\ \frac{6500\left[\right(x+15)-x]}{x(x+15)}=30 \\ x(x+15)=\frac{6500\times 15}{30} \\ {x}^2+15x-3250=0 \\ (x+65)(x-50)=0 \\ x=-65,50 \end{gathered}$$

But, $x=-65$ is not possible as it leads to negative number of persons.

Therefore $x=50$.

Hence, number of persons are $\mathbf{50}$.