Question

# Sheelaâ€™s age is 4 years less than half of her mother's age. Sheela is 2 years less than thrice the age of her younger brother. If Sheela is 13 years old, then find the age of her brother and that of her mother.

Hint: In order to solve this problem we need to know that Sheelaâ€™s motherâ€™s age is four years more than half of her motherâ€™s age and her brotherâ€™s age is two years more than one third of her age. By assuming variables for her motherâ€™s and brotherâ€™s age we can get the right solution.

It is given that Sheela is 13 years old.
Let her motherâ€™s age be M and her brotherâ€™s age be B.

It is given that Sheelaâ€™s age is 4 years less than half of her mother's age.
So, the equation can be made as:
$\dfrac{{\text{M}}}{{\text{2}}}$-4= 13
M = 2(13+4)
M=34 years

It is also given that Sheela is 2 years less than thrice the age of her younger brother.
Therefore, 3B - 2 = 13
3B = 15
B = 5 years
Hence, the age of her mother is 34 years and the age of her brother is 5 years.

Note: Whenever you face such types of problems you have to consider the unknown ages as variables and then make the equations according to the conditions provided. Then solve the equations to get the ages of variables. Proceeding in this way will give you the right answer.