The sum of two numbers is $135$ and the numbers are in the ratio $4:5$. Find the numbers.

In a certain fraction, the denominator is $4$ less than the numerator. If $3$ is added to both the numerator and denominator, the resulting fraction is equal to $\frac{9}{7}$. Find the original fraction.

Divide $489$ into two parts such that the first part is $9$ more than twice the second part.

I have $60$ more one-rupee coins than $₹5$ coins. If the total value of the money is $₹360$, how many $₹5$ coins do I have?

Meera's mother is four times as old as Meera. After five years, her mother will be three times as old as Meera. What are their present ages?

The sum of the present ages of Mohan and Shyam is $60$ years. If the ratio of their present ages is $7:8$, find their present ages.

In a class of $41$ students, the number of girls is $7$ more than boys. How many girls are there in the class?

The ratio of tens digit to ones digit of a two-digit number is $2:3$. If $27$ is added to the number, the digits interchange their places. Find the number. 

The ones digit of a two-digit number is twice the tens digit. If $18$ is added to the number, the digit get reversed. Find the number.