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Home » 6. Rs. 9000 were divided equally among a certain number of persons. Had there been 20 more persons, each would have got Rs. 160 less. Find the original number of persons
6. Rs. 9000 were divided equally among a certain number of persons. Had there been 20 more persons, each would have got Rs. 160 less. Find the original number of persons
CBSE | Class 10 | Maths | Maths | Quadratic Equations | Quadratic Equations | RD Sharma
6. Rs. 9000 were divided equally among a certain number of persons. Had there been 20 more persons, each would have got Rs. 160 less. Find the original number of persons

Solution:

Let’s consider the original number of people as ‘a’.

Given that, Rs.9000 were divided equally among a certain number of persons. Had there been 20 more persons, each would have got Rs.160 less.

Amount which each receives when a persons are present = 9000/a

Expressing the given condition we have,

⇒ 9000a = (9000 - 160a)(a + 20)

    \[9000a=9000a+180000-160{{a}^{2}}-3200a\]

{{a}^{2}}+20a-1125=0

{{a}^{2}}+45a-25a-1125=0

⇒ a(a + 45) - 25(a + 45) = 0

⇒ (a - 25)(a + 45) = 0       

⇒ a = 25 or a = -45 (neglected as the number of people can never be negative)

Therefore, the original number of people = 25.

i

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