Rs. 250 is divided equally among a certain number of children. If there were 25 children more, each would have received 50 paise less. Find the number of children.

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Solution

Let the number of children be x.
It is given that Rs 250 is divided amongst x students.
$S o comma m o n e y space r e c i e v e d space b y space e a c h space c h i l d space equals 250 over x R s I f space t h e r e space w e r e space 25 space c h i l d r e n space m o r e space comma t h e n M o n e y space r e c i e v e d space b y space e a c h space c h i l d equals fraction numerator 250 over denominator x plus 25 end fraction space R s F r o m space t h e space g i v e n space i n f o r m a t i o n 250 over x minus fraction numerator 250 over denominator x plus 25 end fraction equals 50 over 100 fraction numerator 250 x plus 6250 minus 250 x over denominator x left parenthesis x plus 25 right parenthesis end fraction equals 1 half fraction numerator 6250 over denominator x squared plus 25 x end fraction equals 1 half x squared plus 25 x minus 12500 equals 0 left parenthesis x plus 125 right parenthesis left parenthesis x minus 100 right parenthesis equals 0 x equals negative 125 comma 100$

Since, the number of students cannot be negative, so x= -125 is inadmissible.

Hence x = 100. $∴$ The number of students are 100

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