Question

The present age of Prabha’s mother is three times the present age of Prabha. After 5 years their ages will add to 66 years. Find their present ages.

Answer 1

Hint: This is an aptitude question. To solve this question first we will assume Prabha’s age as x and then will determine her mother’s present age and their ages after 5 years in terms of x. Then taking the addition of their ages after 5 years as 66 years we will get an equation and solve that we will get the value of x, thus we will get their present ages.

Complete step-by-step answer:
Let the present age of Prabha be x.
According to the question, the present age of Prabha’s mother is three times the present age of Prabha.
So, let the present age of Prabha’s mother be $ 3x $ .
After 5 years Prabha’s age will be $ x + 5 $
And after 5 years Prabha’s mother’s age will be $ 3x + 5 $
According to the question, after 5 years their ages will add to 66 years.
Hence, $ (x + 5) + (3x + 5) = 66 $
Expanding the above equation we get,
 $ x + 5 + 3x + 5 = 66 $
Adding the similar terms of the left hand side of the above equation we get,
 $ 4x + 10 = 66 $
Subtracting 10 from the both of the side,
 $ 4x + 10 - 10 = 66 - 10 $
 $ \Rightarrow 4x = 56 $
Dividing 4 in both of the side,
 $ \dfrac{{4x}}{4} = \dfrac{{56}}{4} $
 $ \therefore $ $ x = 14 $
As we have taken x as the present age of Prabha earlier, so the present age of Prabha is 14 years.
 $ \therefore $ The present age of Prabha’s mother is, $ 3x = 3 \times 14 = 42 $ years

Therefore, the present ages of Prabha and Prabha’s mother are 14 years and 42 years respectively.

Note: This aptitude question is a linear equation question having one variable and constants.
You should practice more linear equations.
You can also do this question in an alternative method in which first we will subtract 10 from 66 as it is the sum of the both of the ages after 5 years, then dividing the result by 4 we will get the age of Prabha and thus we will get the age of her mother. We divide it with 4 because the mother’s age is 3 times of daughter’s age, so taking it as a sum total of $ 3 + 1 = 4 $ units.