Question

A scholarship account of Rs 75,000 was distributed equally among a certain number of students. Had there been 10 students more, each would have got Rs 250 less. Find the original number of persons. 

Answer 1

Let the original number of students be S.

 Original amount that the student got = `75000/"S"`

In new scenario, 5 increased to 5+10, Amount reduced by 250. 

`=> 75000/"S" - 75000/("S" + 10) = 250`

Dividing by 250 throughout the equation, we get: 

`300/"S" - 300/("S" + 10) = 1`

⇒ 300 S + 3000 - 300 S = S² + 105 

⇒ S² + 105 - 3000 = 0 

⇒ S²+605 - 505 - 3000 = 0 

⇒ S (S + 60) - 50 (S + 60) = 0 

⇒ (S + 60) (5 - 50) = 0 

⇒ S = -60 , 50

Number of students cannot be negative. 

Hence number of students = 50