Question

Vidhi is $10$ years older than Tithi. Tithi is $2$ years younger than Swati but $1$ year older than Ekta. Their ages add up to a number which is a multiple of $3$ between $121$ and $125$. Find the present age of each.

Answer 1

Hint: We will solve the given question by assigning variables to the information which is not known to us. Here we have to find the present age as it is unknown to us and hence we will assign variables to it. It must also be kept in mind that for different objects or people, different variables shall be assigned.

Complete step by step solution:
Let the present age of Vidhi be $w$ years, the present age of Tithi be $x$ years, the present age of Swati be $y$ years and the present age of Ekta be $z$ years.
From the information given in the question, we know that Vidhi is $10$ years older than Tithi. On converting this information into an equation, we will get
$w = x + 10$ {equation (1)}
Moreover, we know that Tithi is $2$ years younger than Swati. On converting this information into an equation, we will get
$y = x + 2$ {equation (2)}
Also, Tithi is $1$ a year older than Ekta. On converting this information into an equation, we will get
$z = x - 1$ {equation (3)}
Now we have to find a number between $121$ and $125$ which is a multiple of $3$. For this we will see which of the numbers among $122$, $123$ and $124$ is divisible by $3$, such that
$\dfrac{{122}}{3} \ne m$ and $\dfrac{{123}}{3} = m = 41$ and $\dfrac{{124}}{3} \ne m$ where $m$ is an integer.
Hence, from the question we obtain the fact that their ages add up to $124$, such that
$w + x + y + z = 124$
On substituting equation (1), equation (2) and equation (3) in the above equation, we will get
$ \Rightarrow (x + 10) + x + (x + 2) + (x - 1) = 123$
$ \Rightarrow 4x + 11 = 123$
On subtracting $11$ from both sides, we will get
$ \Rightarrow 4x = 112$
On dividing both the sides by $4$, we will get
$ \Rightarrow x = \dfrac{{112}}{4}$
$ \Rightarrow x = 28$
So on substituting this value of $x$ in equation (1), we will get
$ \Rightarrow w = 28 + 10$
$ \Rightarrow w = 38$
Further on substituting this value of $x$ in equation (2), we will get
$ \Rightarrow y = 28 + 2$
$ \Rightarrow y = 30$
Also on substituting this value of $x$ in equation (3), we will get
$ \Rightarrow z = 28 - 1$
$ \Rightarrow z = 27$

Hence, the present age of Vidhi is $38$ years, the present age of Tithi is $28$ years, the present age of Swati is $30$ years and the present age of Ekta is $27$ years.

Note:
We can cross-check the answers by putting them into the equations that we have formed while solving the question. When we substitute the values of the answer, we must get the left hand side equals to the right hand side of the equation. Then only the answer is said to be correct otherwise it is not.