Egg problem-Brain Teaser-Amazon Interview Question

Question

A lady from the chicken farm gathers the eggs and brings it to sell it in the market.
She sells the eggs but few eggs are left over.
The 2nd day the left over eggs was doubled.
Yet she sells the same amount of eggs as the 1st day.
The 3rd day the left over eggs was tripled.
Yet she sells the same amount of eggs as the 1st day.
The 4th day the left over eggs was quadrupled.
Yet she sells the same amount of eggs as the 1st day.
The 5th day the left over eggs was quintupled.
Yet she sells the same amount of eggs as the 1st day. And the remaining eggs where disposed

Question How many eggs did she take to the market on the 1st day and how many was left over?

Answer 1

Hint: Let $x$ be the original number of eggs and $y$ be the number sold each day. After the doubling on the second day she has $2(x-y)$ eggs. After the tripling on the third day she has $3(2(x-y)-y)$ eggs. Keep going. Usually in problems like this you are given that the process comes out even on the last day. Otherwise you don't have enough information to solve the problem. In this case, for a given $y$, we can always increase $x$ by $1$ and the remainder by $120$ (why that?) and have another solution.