Question

Reena is 6 years older than her brother Ajay. If the sum of their ages is 28 years. What are their present ages?

Answer 1

Hint: We start solving the problem by assigning variables to the age of the Ajay. We then find the age of Reena by using the condition that Reena is 6 years older than her brother Ajay. We then add both the obtained ages and equate it to the given 28 years. We then make the necessary calculations to get the required ages of Reena and Ajay.

Complete step-by-step answer:
According to the problem, we are given that Reena is 6 years older than her brother Ajay and the sum of their ages is 28 years. We need to find their present ages.
Let us assume the age of Ajay is ‘x’ years. Now, we are given that Reena is 6 years older than Ajay which means that the age of Reena is 6 years more than the age of Ajay. So, the age of Reena is \[x+6\] years.
According to the problem, we are given that the sum of ages of Reena and Ajay is 28 years.
So, we get $x+x+6=28$.
$\Rightarrow 2x=22$.
$\Rightarrow x=\dfrac{22}{2}$.
$\Rightarrow x=11$ years.
So, we have found the age of Ajay as 11 years.
Now, let us find the age of Reena.
So, we get Reena’s age as $x+6=11+6=17$ years.
∴ The ages of Reena and Ajay are 17 years and 11 years.

Note: Whenever we get this type of problems, we assign the variables to the unknowns that were present in the problem. We should not confuse between the younger and older while solving this type of problem. We should not stop solving the problem after finding the age of Ajay as this is the most common mistake done by students. Similarly, we can expect the problems to find the age of Ajay at which Reena’s age is twice of Ajay.