Dividing Rs.69 among 115 students, each girl gets 50 paise less than a boy; each boy gets twice the paise as each girl. How many girls in the class?

Question:

Rs.69 were divided among 115 students so that each girl gets 50 paise less than a boy. Thus each boy received twice the paise as each girl received. The number of girls in the class is?

Doubt:

Here my solution manual wonderfully assumed money per girl is 50 and money per boy as 100. How can we be so sure about the values by merely looking at the question? Some guidance about the same is most certainly welcome.

Solution 1:

Because each girl gets $50$ paise less than a boy and we are also told that each boy gets twice as many paise as a girl. The only way that an amount plus $50$ is twice that amount is when the amount is $50$. In other words, if a number plus $50$ is twice the number then that number can only be $50$ ($x+50=2x\iff x=50$).