Question

please solve fast
it's urgent

Answer 1

Let the no. of students = y

Given, each student is given equal amount of money.

Let the amount distributed to each = z

Then, Total money = yz

A/Q 1. If there are 8 less prize winners, amount won by each increases by 10

=> (y - 8) (z + 10) = yz
=> yz + 10y - 8z - 80 = yz
=> 10y - 8z - 80 = 0
=> 10y - 8z = 80 ...(1)

2. If there are 16 more prize winners, everyone gets amount 10 less.

=> (y + 16) (z - 10) = yz
=> yz - 10y + 16z - 160 = yz
=> - 10y + 16z - 160 = 0
=> - 10y + 16z = 160...(2)

Combining equations (1) and (2)

=> 10y - 8z + (-10y) + 16z = 80 + 160
=> 8z = 240
=> z = 30

Finding y by substituting,

10y - 8z = 80
=> 10y - 240 = 80
=> 10y = 320
=> y = 32

So the no. of prize winners is 32 and money each one of them gets is Rs. 30.
Total amount = No. of participants * amount given to each
= 32 * 30
= 960

Thus the total amount was Rs. 960.