Question

The ages of Sonu and Monu are in the ratio $ 7:5 $ . Ten years hence, the ratio of their ages will be $ 9:7 $ . Find their 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 ages of Sonu and Monu. It is given that the ratio of their ages is $ 7:5 $ .
Let us assume the present age of Sonu be $ 7x $ and the present age of Monu be $ 5x $ . After ten years their age will increase, so it will be the Age of Sonu $ = 7x + 10 $ and the age of Monu will be $ 5x + 10 $ .
Now substituting according to the question, we have: $ \dfrac{{7x + 10}}{{5x + 10}} = \dfrac{9}{7} $ . We will solve it now by applying the cross multiplication, $ 7(7x + 10) = 9(5x + 10) \Rightarrow 49x + 70 = 45x + 90 $ .
We will solve for $ x $ , It gives us
$ 49x - 45x = 90 - 70\\
 \Rightarrow 4x = 20
 $ .
So the value is $ x = \dfrac{{20}}{5} = 5 $ . By putting the value of $ x $ in their ages: Present age of Sonu is $ 7 \times 5 = 35 $ .Present age of Monu is $ 5 \times 5 = 25 $ .
Hence the present age of Sonu is $ 35 $ years and the present age of Monu is $ 25 $ years.

Note: We should always be careful what the question is asking i.e. present ages of Sonu and Monu. 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 cross multiplication 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.