Question

Rs. 7500 is divided equally among a certain number of children. Had there been 20 less children, each would have receive Rs 100 more. Find the original number of children. 

Answer 1

Let the original number of person be x, then 7500 divided equally between x person,

each one gets = `7500/x`

7500 divided equally between x - 20 children

each one gets 75 = `7500/ (x-20)`

According to the question 

`7500/(x-20)=7500/x+100/1`

`7500/(x-20)=(7500+100x)/x`

7500 = (x - 20) (7500 + 100x)

75x = (x - 20) (75 + x)

75x = 75x + x² - 1500 - 20x

x² - 20x - 1500 = 0

x = `(20±sqrt(400-4(-1500)))/2`

x = `(20±sqrt(400+6000))/2`

x = `(20±80)/2`

x = `(20+80)/2` or x = `(20-80)/2`

x = 50 or x = -30 (not possible)

∴ Original number of children = 50