Word Problems on Quadratic Equation

A dealer sells a toy for $₹24$ and gains as much percent as the cost price of the toy. Find the cost price of the toy in rupees.

Two women together took $100$eggs to a market, one had more than the other. Both sold them for the same sum of money. The first then said to the second: "If I had your eggs, I would have earned $₹15$, to which the second replied: "If I had your eggs, I would have earned $₹6\frac{2}{3}$". How many eggs did each have in the beginning?

A shopkeeper buys a number of books for $₹ 800$. If he had bought $4$ more books for the same amount, each book would have cost $₹ 10$ less. How many books did he buy?

The sum of ages of a woman and her daughter is $40$ years. The product of their ages five years ago was $125$ years. If the present age of the woman is $k$ years then, write the value of $k$ as final answer.

A two digit number is such that the product of its digits is $35$. When $18$ is added to the number, the digits interchange their places. Find the number.

If the sum of squares of two consecutive integers is $85$. What is the product of these two consecutive integers?