Question

Rahul mother's present age is six times Rahul's present age. Rahul's age five years from now will be one-third of his mother's present age. What are their present ages?
(a) Present age of Rahul is 8 years and that of his mother is 48 years
(b) Present age of Rahul is 9 years and that of his mother is 54 years
(c) Present age of Rahul is 5 years and that of his mother is 30 years
(d) Present age of Rahul is 4 years and that of his mother is 24 years

Answer 1

- Hint: To solve this problem, we will use two variables (x and y) to represent the above problem. We will represent x as Rahul’s present age and y to be his mother’s present age. We will then use the relation that Rahul's age five years from now will be one-third of his mother's present age to solve the algebraic equations and get the value of x and y.

Complete step-by-step solution -

For solving this question, we first try to convert the word problem into algebraic equations. Thus, according to first condition, it is given that Rahul mother's present age is six times Rahul's present age, thus, we have,
y = 6x (here, x represents Rahul’s present age and y represents Rahul’s mother’s present age) -- (1)
Now, we also know that Rahul's age five years from now will be one-third of his mother's present age, thus, we have that,
(x+5) = $\dfrac{1}{3}$ (y) -- (2)
Now, we have to solve equations (1) and (2), we substitute y = 6x from (1) into (2), we get,
x + 5 = $\dfrac{1}{3}$ (6x)
x + 5 = 2x
x = 5
Also, y = 6x = 30
Thus, Rahul’s present age is 5 years and his mother’s present age is 30 years.
Hence, the correct answer is (c).

Note: In most of the algebraic problems, it is important to convert the problem in English into mathematical equations. Once, that is done, one can solve it manually or use matrix algebra to solve the problem. Generally, for an equation with 2 variables and 2 unknowns, we solve manually, while for a higher number of variables, we generally use matrix algebra. In this problem, since there were 2 equations and 2 variables, we solved the algebraic equations manually.