Question

The age of Rahul and Haroon are in the ratio 3:5. Seven years later the sum of their ages will be 62 years. What are their present ages?

Answer 1

Hint: In order to solve this question we will first put the ratio of their ages in fraction then we will find the relation of their from this fraction then 7 years later we will put the summation of their ages equal to 62 and we will replace one value and find the age of one of these two and find the others age through the relation.

Complete step by step solution:
For solving this question we will first let the age of Rahul to be x and the age of Haroon to be y now according to the question as it is given that the ratio of age of Rahul to the Haroon is 3:5 so writing it in fraction:
 $ \dfrac{x}{y} = \dfrac{3}{5} $
Now we will find the relation on these two so:
 $ 5x = 3y $
Now putting only x in a side and replacing other things other side we will get:
 $ x = \dfrac{3}{5}y $ …………..(1)
Now as it is given that 7 years the summation of their ages will be 62, so seven years later the age of Rahul will be x+7 and similarly the age of Haroon will be y+7 so will get the equation:
 $ \left( {x + 7} \right) + \left( {y + 7} \right) = 62 $
On further solving this we will get:
 $ x + y + 14 = 62 $
Now substituting 14 to other side we will get:
 $ x + y = 48 $ ……………(2)
Now putting the value of x from equation 1 to equation 2:
 $ \dfrac{3}{5}y + y = 48 $
On further solving:
 $ \dfrac{8}{5}y = 48 $
Now on finalizing it we will get:
 $\Rightarrow y = 30 $
From equation we will get the value of x:
 $\Rightarrow x = \dfrac{3}{5} \times 30 $
The value of x will be 18.
So the present age of Rahul will be 18 years and the age of Haroon will be 30 years.
So, the correct answer is “So the present age of Rahul will be 18 years and the age of Haroon will be 30 years”.

Note: While solving these types of problems always keep in mind that we always make the equation how many unknowns are there and from there we will find the relation in the unknowns. One common mistake done by students is that we let the present age be x and y but when it is told that 7 years later or 5years ago we forget to add 7 or subtract 5 so this thing should be kept in mind.