Question

The present age of a man is twice that of his son. Eight years hence, their ages will be in the ratio $ 7:4 $ . Find the son’s present ages.

Answer 1

Hint: As we know that the above given question is a word problem. A problem is a mathematical question written as one sentence or more describing a real life scenario where that problem needs to be solved by the way of mathematical calculation. We can solve the given problem by applying the method of mathematical equations and then simplify it.

Complete step by step solution:
We need to first understand the requirement of the question which is the present age of son’s.
Let us assume that the present age of the son is $ x $ . Now in the question we have been given that the present age of a father is twice of the present age of his son. So we can say that the present age of a father is $ 2x $ .
We have been given the question that the ratio of their ages after eight years is
 $ 7:4 $ i.e. $ \dfrac{7}{4} $ .
So their ages after eight years will be
 $ \dfrac{{2x + 8}}{{x + 8}} = \dfrac{7}{4} $ .
Now we will solve this by the cross multiplication: $ 4(2x + 8) = 7(x + 8) $ .
By breaking the brackets we can multiply each term and we can write it as
 $ 4 \times 2x + 4 \times 8 = 7 \times x + 7 \times 8 \Rightarrow 8x + 32 = 7x + 56 $ .
We will bring the similar terms together and then solve it by isolating the term $ x $ , :
 $ 8x - 7x = 56 - 32 \Rightarrow x = 24 $ .
Hence the present age of son i.e. $ x = 24 $ years.
So, the correct answer is “ $ x = 24 $ years”.

Note: We should always be careful what the question is asking i.e. the present age of son after $ 8 $ years, so when will calculate the present age the eight years will also be added. Based on the requirement and by observing all the necessary information that is already available in the question we gather the information and then create an equation or by unitary method whichever is applicable, then we solve the problem and then verify the answer by putting the value in the problem and see whether we get the same answer or not.