Question

A man starts with his job with a certain monthly salary and earns a fixed increment every year. If his salary was Rs. \[1500\] after 4 years of service and Rs. $1800$ after 10 years of his service, what was his starting salary and what is the annual increment?

Answer 1

Hint: We start solving this question by assuming the starting salary be $x$ and annual increment by $y$. Then, by using the information given in the question that his salary was Rs. \[1500\] after 4 years of service and Rs. $1800$ after 10 years of service, we form the equations and solve these equations to get the answer.

Complete step by step solution:
We have given that a man starts with his job with a certain monthly salary and earns a fixed increment every year.
Let us assume that the starting salary is $x$ and the annual increment by $y$.
Also, we have given that after 4 years of service his salary was Rs. \[1500\].
So, the equation will be $x+4y=1500...........(i)$
Also, we have given that after 10 years of service his salary was Rs. $1800$.
So, the equation will be $x+10y=1800...........(ii)$
Now, we have two equations in two variables. To solve these equations we subtract equation (i) from equation (ii), we get
$\begin{align}
  & \Rightarrow x-x+10y-4y=1800-1500 \\
 & \Rightarrow 6y=300 \\
 & \Rightarrow y=\dfrac{300}{6} \\
 & \Rightarrow y=50 \\
\end{align}$
We have to put the value of $y$ in equation (i) to get the value of $x$
$\begin{align}
  & x+4y=1500 \\
 & \Rightarrow x+4\times 50=1500 \\
 & \Rightarrow x+200=1500 \\
 & \Rightarrow x=1500-200 \\
 & \Rightarrow x=1300 \\
\end{align}$
So, the starting salary is Rs. $1300$ and annual increment is Rs. $50$.

Note: This question is based on the concept of linear equation in two variables because there are two unknown quantities. To find the value of two unknown quantities we need two equations. Here in this question, we solve the equations by using the elimination method. Alternatively, we can solve the equations by using the substitution method. From equation (i) we can substitute the value $x=1500-4y$ in the equation (ii) to get the value of $y$.