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प्रश्न
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.
उत्तर
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
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