Question

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.

Answer 1

SOLUTION :  

Let the original number of persons be x.

Share of each person = ₹ 9000/ x ……(1)

If the number of person is increased by 20, then

New Share of each person = ₹ 9000/(x+20)……(2)

On Solving eq 1 and 2,

9000/x - 9000/(x+20) = 160  

[each person gets ₹ 160 less if number of person is increased by 20]

(9000 (x+20) - 9000x) / x(x+20)  = 160

[By taking LCM]

9000x + 9000 × 20 -9000  / x² + 20x = 160

9000 × 20 /x² + 20x=160

180000 / x² + 20x = 160

160(x² + 20x )= 180000  

x² + 20x = 180000/160

x² + 20x =1125

x² + 20x - 1125= 0

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

Since the number of persons cannot be negative. So x = 25

Hence, original number of persons is 25.

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Hey mate,

Let the no. of person be x.

So each person gets = 9000/x Rs

If 20 more person,

Each got = 9000/20+x

So ATQ,

900/20+x = 9000/x - 160

Cross multiply,

x^2 +20x - 1125 = 0

So,

X = - 45, 25

No. of person can't be negative so

Total people = 25

Hope this helps you out!