Question

Kinjal tells her sister that 3 years ago, the sum of your age and my age was 36 years. Then, after 4 years, what will be the sum of your age and my age?
A. 53 years
B. 39 years
C. 43 years
D. 50 years

Answer 1

Hint: Here we begin by assuming the age of Kinjal be $x$ and the age of her sister be $y$. Then we use the given condition to form an equation and find the value of $x + y$. Then, find the sum of their ages after 4 years in terms of $x$ and $y$ and then substitute the values of $x + y$ to get the required answer.

Complete step by step answer:

Let the age of Kinjal be $x$ and let the age of her sister be $y$.
Now we are given that the sum of their ages 3 years ago be 36 years.
The age of the Kinjal 3 years ago will be $x - 3$
And the age of her sister will be 3 years ago is $y - 3$
Then, the sum of ages will be $\left( {x - 3} \right) + \left( {y - 3} \right) = 36$ which is equals to 36.
Then, $x - 3 + y - 3 = 36$
That is,
$x + y - 6 = 36$
Adding 6 to both sides,
\[x + y = 42\]........eq. (1)
But, we are asked to find out the sum of their ages after 4 years.
Also, the age of Kinjal after 4 years will be \[x + 4\] and the age of her sister will be \[y + 4\]
We want to the value of \[x + 4 + y + 4\] which is equivalent to writing \[x + y + 8\]
From equation (1) the value of \[x + y\] is 42.
On substituting the value of $x + y$ as 42, we get
\[x + y + 8 = 42 + 8 = 50\]
Hence the sum of their ages after 4 years will be 50 years.
Thus option D is correct.

Note: Students generally make mistakes by adding 4 to the value of $x + y$ to calculate the sum of their ages after 4 years which gives an incorrect answer as 4 will added to both the ages and not just the sum of ages.