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Question
Rs. 6500 was divided equally among a certain number of persons. Had there been 15 persons more, each would have got Rs. 30 less. Find the original number of persons.
Solution
Let the original number of persons be x.
Total money which was divided = Rs. 6500
Each person share = Rs. `6500/x`
From the given information
`6500/x - 6500/(x + 15) = 30`
`3250/(x(x + 15)) = 1`
x2 + 15x – 3250 = 0
x2 + 65x – 50x – 3250 = 0
x(x + 65)(x – 50) = 0
x = –65, 50
Since, the number of persons cannot be negative.
Hence, the original number of persons is 50.
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