The compound interest on the sum of money at 8% p.a. for 2 yrs is more than the simple interest on the same sum at the same rate for the same time by Rs 72.80. find the sum.

25201 eggs

Step-by-step explanation:

We are told that when the number is divided by 2, 3, 4, 5, 6, 7, 8, 9, 10 there is 1 egg left.

Thus means we have to find the Least common multiple(L.C.M)

L.C.M of 2, 3, 4, 5, 6, 7, 8, 9, 10 is 2520

Since when divided by the numbers above, we have 1 egg remaining, it means the formula to get the total number of eggs will be;

2520x + 1

Where x is any positive integer.

Now, we are told that when you divide the number of eggs by 11 there will be no eggs left.

This is modulo 11.

It means we have to find the smallest number of X for which 2520x + 1 modulo 11 is 0.

The smallest number will be at x = 10

Thus:

Number of eggs = 2520(10) + 1 = 25201

To confirm this; 25201/11 = 2291

No remainder, so it shows that that is truly the number of eggs