Two numbers are in the ratio $5:6$. If $8$ is subtracted from each of the numbers,the ratio becomes $4:5$. Find the numbers.

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.

Find the value$(s)$ of $p$ for the pair of equations $-x + py = 1$ and $px - y = 1$ if the system has no solution.

The solution set of the pair of equations $x = -2$ and $y = 3$ is:

$A$ fraction becomes $\frac{1}{4}$ if $2$ is subtracted from the numerator and $3$ is added to the denominator. If $6$ is added to the numerator and the denominator is multiplied by $3$,it becomes $\frac{2}{3}$. Find the fraction.

Four years ago,the sum of the ages of a mother and her two daughters was $x$ years. What will be the sum of their ages after two years?