Question

Raveena is 7 years older than her sister Praveena. The sum of their ages six years later will be 35. Find their present ages.

Answer 1

Hint: Assume the ages of Raveena and Praveena as x and y years respectively. Form two linear equations in two variables x and y according to the given conditions and solve them to get the answer. Take $\left( x+6 \right)$ and $\left( y+6 \right)$ as the ages of Raveena and Praveena respectively after six years.

Complete step-by-step solution:
Here, we have been provided with the information regarding the ages of two sisters Raveena and Praveena and we are asked to find their present ages.
Now, let us assume the present age of Raveena is x years while that of Praveena is y years. So, here we are provided with two cases, let us check them one-by-one.
(1) Case 1: Here it is said that at present time Raveena is 7 years older than Praveena, so forming a linear equation, we get,
$\Rightarrow x=7+y\ldots \ldots \ldots \left( i \right)$
(2) Case 2 : Now, it is said that after six years the sum of their ages will be 35. So, we have,
$\Rightarrow $ Age of Raveena after six years $=x+6$
$\Rightarrow $ Age of Praveena after six years $=y+6$
Therefore, taking the sum of their ages and equating with 35, we get,
$\begin{align}
  & \Rightarrow \left( x+6 \right)+\left( y+6 \right)=35 \\
 & \Rightarrow x+y+12=35 \\
 & \Rightarrow x+y=35-12 \\
 & \Rightarrow x+y=23\ldots \ldots \ldots \left( ii \right) \\
\end{align}$
Now, substituting the value of x from equation (i) in equation (ii), we get,
$\begin{align}
  & \Rightarrow y+7+y=23 \\
 & \Rightarrow 2y=23-7 \\
 & \Rightarrow 2y=16 \\
 & \Rightarrow y=8 \\
\end{align}$
Substituting the value of y in equation (i), we get,
$\begin{align}
  & \Rightarrow x=7+8 \\
 & \Rightarrow x=15 \\
\end{align}$
Hence, the present ages of Raveena and Praveena are 15 years and 8 years respectively.

Note: One may note that we can also solve the above question without considering the second variable y. We can directly assume the age of Raveena and Praveena as x and (x - 7) respectively and form a single linear equation in one variable x to get the answer. You may see that we have used the substitution method to solve the above obtained linear equations. You can also use the method of cross multiplication or elimination method to get the answer.