Question

rupees 9000 were divided equally among a certain number of person.Had there been 20 more persons each would have got rupees 160 less. find the original number of persons

Answer 1

Original number of persons—n
: 9,000/n - 160 = 9,000/(n + 20)
(9,000 - 160n)/n = 9,000/(n + 20)
9,000n = 9,000n - 160n² + 180,000 -3,200n
n² + 10n = 1,125 + 10²
n² + 10n = 1,125 + 100
(n + 10)² = 1,225
n + 10 = 35
n = 25

Answer: 25 persons originally

Answer 2

HERE IS YOUR ANSWER...⬇⬇



$\underline{SOLUTION}$ ➡


Given,

Sum of money to be divided = Rs.9000

Let,

The original number of person = x

A.T.Q.,

$\frac{9000}{(x + 20) } = \frac{9000}{x} - 160 \\ \\ = > \frac{9000}{(x + 20)} = \frac{9000 - 160x}{x} \\ \\ = > 9000x = (9000 - 160x)(x + 20) \\ \\ = > 9000x = 9000(x + 20) - 160x(x + 20) \\ \\ = > 9000x = 9000x + 180000 - 160x {}^{2} - 3200x \\ \\ = > 160x {}^{2} + 9000x - 9000x + 3200x - 180000 = 0 \\ \\ = > 160x {}^{2} + 3200x - 180000 = 0 \\ \\ = > x {}^{2} + 20x - 1125 = 0\\ \\ => x {}^{2} + 45x - 25x - 1125 = 0 \\ \\ => x(x+45)-245(x+45) = 0 \\ \\ => (x+45)(x-25) = 0$



•°• x + 45 = 0

=> x = - 45


Or,


x - 25 = 0

=> x = 25


Here,

x is not equal to ( - 45 )


•°• x = 25


So,

The original number of persons = 25



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