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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?

#### APPEARS IN

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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