In a cricket stadium, the people are made to sit to watch the match. If the organisers make a row of 15 people each, there will be 10 people left. If they make rows of 20 people each then there will be 15 people left and if they make rows of 24 people each, 19 people will be left. If they make rows of 28 people each there will be 23 people left. Find the minimum number of people present in the stadium.

Let the total number of people be X. 

1) When X is divided by 15, we get a remainder of 10. Hence, X = 15a + 10

2) When X is divided by 20, we get a remainder of 15. Hence, X = 20b + 15

3) When X is divided by 24, we get a remainder of 19. Hence, X = 24c + 19

4) When X is divided by 28, we get a remainder of 23. Hence, X = 28d + 23

This is a classic case when the difference between the divisor and remainder is the same, which is 5 in this case. In such instances, the number is expressed as (LCM of the divisors)$$\times$$K - (difference between the divisors and remainders).

Hence, the number of people shall be 840k - 5.

The minimum number is when k=1, hence the minimum number shall be 835.