Question

The ratio of present ages of Ajay and Vijay are in the ratio 4:5. After 8 years the ratio of their ages will be in the ratio 5:6, then find their present ages.

Answer 1

Hint – In order to find their present ages, we consider the ratio of their present age and multiply them with a variable to obtain their individual ages in present. Then we add their ages by 8 and put them in the ratio of ages after 8 years to determine the value of the variable which gives us the present ages.

Complete step-by-step answer:
Given data,
The present ratio of ages is 4:5
After 8 years their ages are in the ratio 5:6.
According to the ratio of present ages, let us consider a variable ‘x’ such that their present ages are 4x, 5x respectively.
Therefore their ages after 8 years are –
We add 8 years to their present ages.
I.e. 4x+8 and 5x+8 respectively.
Given their ratio of ages after 8 years is 5:6
Therefore we get,
(4x+8): (5x+8) = 5:6
$ \Rightarrow \dfrac{{{\text{4x + 8}}}}{{{\text{5x + 8}}}} = \dfrac{5}{6}$
⟹6 (4x+8) = 5 (5x+8)
⟹24x + 48 = 25x + 40
⟹x = 8.
Therefore their present ages are 4x, 5x i.e. 4(8) and 5(8), 32 years and 40 years respectively.

Note – In order to solve this type of question the key is to know the meaning of the ratio of two numbers. If two numbers a and b are said to be in the ratio x: y. Then that means the value of a divided by b is equal to the value of x divided by y. It is given as$\dfrac{{\text{a}}}{{\text{b}}} = \dfrac{{\text{x}}}{{\text{y}}}$, which can also be written as ay = bx.
It can also be defined as how many times the first number is of the second.
Here considering a variable x and performing operations on it is a crucial step, we used the variable to create a relation between present and ages after 8 years and solved for the value of x to find the present ages.