Answer:
20
Explanation:
Let the number of people be x.
Rs. 1000 is distributed equally among x people, so each person gets 1000/x.
If there were 5 people more, there would be x + 5 people.
Then, each person would get 1000/(x + 5). Each of the x + 5 people would get Rs. 10 less than before.
1000/x - 10 = 1000/(x + 5)
Multiply both sides by the LCD, x(x + 5).
x(x + 5) × 1000/x - x(x + 5) × 10 = x(x + 5) × 1000/(x + 5)
(x + 5) × 1000 - (x² + 5x) × 10 = x × 1000
1000x + 5000 - 10x² - 50x = 1000x
5000 - 10x² - 50x = 0
10x² + 50x - 5000 = 0
x² + 5x - 500 = 0
(x + 25)(x - 20) = 0
x + 25 = 0 or x - 20 = 0
x = -25 or x = 20
The actual number of people is 20.
Check:
Rs. 1000/20 = Rs. 50
Rs. 1000 divided equally among 20 people gives Rs. 50 per person.
If there are 5 people more, then there are 25 people.
Rs. 1000/25 = Rs. 40
Rs. 1000 divided by 25 people gives Rs. 40 per person which is Rs. 10 less per person.
Our solution is correct.