Answer :

Let the no of children is x and amount given to each child is y


As the total amount is 250 ₹


We have,


xy = 250


…[1]


Also, given if no of children is increased by 25, the amount to each get less by 50 paise i.e. 0.5 ₹


So, we have


(x + 25)(y – 0.5) = 250


[By 1]



500x – x2 + 12500 – 25x = 500x


x2 + 25x – 12500 = 0


x2 + 125x – 100x – 12500 = 0


x(x + 125) – 100(x + 125) = 0


(x – 100)(x + 125) = 0


so,


x – 100 = 0 or x + 125 = 0


x = 100 or – 125


However, no. of students can't be negative


Hence, x = 100


So, there were 100 students.


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