Question

₹9000 is equally divided among a certain number of persons .Had there been 20 more person ,each would have got ₹160 less.Find the original number of person

Answer 1

Let the original number of students = x
Total amount to be divided = Rs. 9000

share of each student = Rs. [9000x]
When the number of students increased by 20 :

number of students = (x + 20)

share of each student =Rs. [9000x + 20]According to the question,9000x − 9000x+20 = 160⇒9000[1x − 1x + 20] = 160⇒[1x − 1x + 20] = 1609000⇒[x + 20 − xx (x + 20)] = 4225⇒20x2+ 20x = 4225
⇒x2 + 45x − 25x − 1125 = 0⇒x(x + 45) − 25(x + 45) = 0⇒(x − 25) (x + 45) = 0⇒x − 25 = 0    or   x + 45 = 0⇒x = 25       or  x = −45 [rejected]So, original number of students = 25

Answer 2

the total amount is 9000.

number of people= x

amount of money received by one person= 9000/x

if 20 person were more= x+20

now, 9000/x + 9000/(x+20) = 160

=> (x +x+20)/x^2+20x = 4/225

=> 225(2x+20)= 4(x^2 + 20x)

=> 450x + 4500 = 4x^2 + 80x

=> 2x^2 - 185x - 2250 = 0

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