Question

The age of a father 10 years ago was thrice the age of his son. Ten years hence, a father's age will be twice that of his son. The ratio of their present ages is
A. 5: 2
B. 7: 3
C. 9: 2
D. 13: 4

Answer 1

Hint: In this question we will make a linear equation in one variable by using single variable x. As it is given in the question that the age of father 10 years ago was thrice the age of his son, so if we take the son’s age as x then automatically the father’s age becomes 3x. Applying the same in the next part we can get our required equation.

Complete step by step answer:
As per the question, we have to find out the ratio of father’s and son’s age respectively.
Let us assume the ages of father and son 10 years ago be 3x and x years,
Then, according to the question, we have to make the equation, that is
(3x + 10) + 10 = 2(x +10) + 10
After solving the above equation, we will get
3x + 20 = 2x + 40
x = 20
Therefore, Required Ratio will be (3x + 10) : (x + 10) = 70 : 30
7 : 3
Now, we have the ratio of their present ages will be 7 : 3

So, the correct answer is “Option B”.

Note: RATIO: In certain situations, the comparison of two quantities by the tactic of division is extremely efficient. We will say that the comparison or simplified sort of two quantities of an equivalent kind is mentioned as ratio. This relation gives us what percentage times one quantity is adequate to the opposite quantity. In simple words, the ratio is that the number which may be wont to express one quantity as a fraction of the opposite ones.
The two numbers during a ratio can only be compared once they have an equivalent unit. We make use of ratios to match two things. The sign won't denote a ratio is ‘:’.
A ratio is often written as a fraction, say $\dfrac{2}{5}$. We happen to ascertain various comparisons or say ratios in our lifestyle .

Key Points to Remember:
1. The ratio should exist between the quantities of an equivalent kind
2. While comparing two things, the units should be similar
3. There should be significant order of terms
4. The comparison of two ratios are often performed, if the ratios are equivalent just like the fractions.