Mahaviracharya/Ganita Sara Samgraha/Chapter VI/95-96

: Chapter $\text {VI}$: Mixed Problems: Problem $95 \frac 1 2$ and $96 \frac 1 2$
Three puranas formed the pay of one man who is a mounted soldier.

At that rate there were $65$ soldiers in all.

Some among them broke down, and the amount of their pay was given to those who remained in the field.

Of this, each man obtained $10$ puranas.

You tell me, after thinking well, how many remained in the field and how many broke down.

Solution

 * $50$ soldiers broke down, while $15$ remained in the field.

Proof
Let $x$ denote the number of soldiers who remained in the field.

Let $y$ denote the number of soldiers who broke down.

We have:

which leaves $65 - 15 = 50$ soldiers who broke down.