Question

Rs 9000 were divided equally among a certain number of persons.Had there been 20 persons more,each would have got Rs160 less.Find the original number of persons.(quadratic equations)
plz solve it.

Answer 1

Let the original no. of persons be x, then
9000 divided equally between x persons, each one get ------> 9000/x
9000 divided equally between (x + 20) persons, each one get------> 9000/(x + 20)
According to the que,
9000/(x + 20) = 9000/x - 160
=> 9000x = (x+20)(9000 - 160x)
=> 9000x = 9000x - 160x^2 + 180000 - 3200x
=> 160x^2 + 3200x - 180000 = 0
=> x^2 + 20x - 1125 = 0
=> x^2 + 45x - 25x - 1125 = 0
=> x(x + 45) - 25(x + 45) = 0
=> (x + 45)(x - 25) = 0
    Either (x + 45) = 0 or ( x - 25) = 0
    (x + 45) = 0 => x = - 45 (not possible)
    Therefore, (x - 25) = 0 => x = 25. ans
   

Answer 2

Answer:

Step-by-step explanation:

Given :-

₹9000 were divided equally among a certain number of persons.

Had there been 20 more persons each would have got ₹ 160 less.

To Find :-

Original number of persons.

Solution :-

Let there be n persons and each get x rupees.

$\sf\implies nx = 9000$

$\sf\implies x=\dfrac{9000}{n}$

According to the Question,

$\sf\implies (n+20)(x-160)=9000$

$\sf\implies (n+20)(\dfrac{9000}{n} -160)=9000$

$\sf\implies 9000+\dfrac{20\times9000}{n}-160n-160\times20=9000$$\sf\implies -160n^2+20\times9000-160\times20n=0$

$\bf\implies n^{2}+20n-1125=0$

$\sf\implies n^{2}+25n-45n-1125=0$

$\sf\implies (n+45)(n-25)=0$

$\bf\implies n=25,-45$

As the original number of persons can't be negative, n ≠ -45.  So n = 25

Hence, the number of persons are 25.