The numerator of a fraction is $4$ less than the denominator. If the numerator is decreased by $2$ and the denominator is increased by $1,$ then the denominator becomes eight times the numerator. Find the fraction.

If the sum and the product of the digits of a two-digit number are the same,then the number is $\ldots \ldots \ldots \ldots$

An employee invests ₹ $x$ at the rate of $5 \%$ and invests ₹ $y$ at the rate of $7 \%$,then he gets ₹ $310$ as yearly interest. Symbolically it is written as ..........

$A$ shopkeeper gives books on rent for reading. She takes a fixed charge for the first two days,and an additional charge for each day thereafter. Latika paid $Rs. 22$ for a book kept for six days,while Anand paid $Rs. 16$ for the book kept for four days. Find the fixed charges and the charge for each extra day (in $Rs.$).

There are some $25$ paise coins and some $50$ paise coins in a bag. The total number of coins is $100$ and the total amount in the bag is Rs. $42.50$. Find the number of coins of each value in the bag.

Vijay had some bananas,and he divided them into two lots $A$ and $B$. He sold the first lot at the rate of $Rs. 2$ for $3$ bananas and the second lot at the rate of $Rs. 1$ per banana,and got a total of $Rs. 400$. If he had sold the first lot at the rate of $Rs. 1$ per banana,and the second lot at the rate of $Rs. 4$ for $5$ bananas,his total collection would have been $Rs. 460$. Find the total number of bananas he had.