The sum of two numbers is $48$ and five times the smaller number is equal to three times the greater number. Find the numbers.

Find two numbers such that the sum of thrice the first number and twice the second number is $102$. Also, five times the first number exceeds thrice the second number by $18$. Find the numbers.

Two numbers are in ratio $4:7$. If $4$ is subtracted from each of the numbers, then the ratio becomes $7:13$. Find the numbers.

Two numbers are in ratio $3:5$. If $5$ is added to each of the numbers, then the ratio becomes $2:3$. Find the numbers.

The sum of two numbers is $20$ and the difference of their squares is $80$. Find the numbers.

The sum of the present ages of Rani and her father is $43$ years. Six years hence, father will be $4$ times as old as his daughter. Find their present ages.

The sum of the ages of Arunima and Kareena is $64$ years. Arunima is $6$ years older than Kareena. Find their present ages.

Five years ago, $A$'s age was $5$ years less than twice $B$'s age. Three years from now, one third of $B$'s age will be $12$ years less than $A$'s age. Find their present ages.