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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. - ICSE Class 10 - Mathematics

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

x^2 + 15x - 3250 = 0

x^2 + 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 s of person is 50

Is there an error in this question or solution?

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Selina Solution for Selina ICSE Concise Mathematics for Class 10 (2018-2019) (2017 to Current)
Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)
Ex.6E | Q: 5

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Solution 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. Concept: Quadratic Equations.
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