rs 6500 is divided equally among a certain number of persons. had there been 15 more persons. each would have got rs30 less. find original number of persons.
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Solution :-
Let the original number of persons be x.
Total amount to be divided = 6500
Share of each = 6500/x
New number of persons = x + 15
New share of each = 6500/x + 15
According to the Question,
⇒ 6500/x - 6500/x + 15 = 30
⇒ 1/x - 1/(x + 15) = 30/6500
⇒ (x + 15) - x/x(x + 15) = 3/650
⇒ 15/(x² + 15x) = 3/650
⇒ 3(x² + 15) = 9750
⇒ x² + 15x = 3250
⇒ x² + 15x - 3250 = 0
⇒ x² + 65x - 50x - 3250 = 0
⇒ x(x + 65) - 50(x + 50) = 0
⇒ (x + 65) (x + 50) = 0
⇒ x + 65 = 0 or x - 50 = 0
⇒ x = - 65, 50 (As x can't be negative)
⇒ x = 50
Hence, the original number of persons is 50.
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