Sum of three consecutive even numbers is $132$, find the numbers.

Sum of three consecutive odd numbers is $159$, find the numbers.

The difference between the squares of two consecutive numbers is $31$. Find the numbers.

Find two consecutive even integers such that twice the smaller exceeds the larger by $18$.

A number is multiplied by $12$ and then added to $60$. The result is $156$. Find the number.

The numerator of a rational number is less than its denominator by $3$. If the numerator becomes three times and the denominator is increased by $20$, the new number becomes $\frac{1}{8}$. Find the original number. 

The numerator of a rational number is $2$ less than the denominator. If $3$ is added to the numerator, the fraction is equal to $\frac{4}{3}$. Find the original number.

The length of a rectangular field is twice of its breadth. If the perimeter of the field be $150 \mathrm{m}$, find the dimensions of the rectangle.