Question

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

Hint: Based on the concept of linear equations in two variables.

Let the starting salary be Rs. X and the annual increment is R.
Now, the problem says the salary will have an yearly increment of R.

According to the question, his salary after 4 years is Rs 1500.
$\Rightarrow {\text{X + 4R = 1500 - (1)}}$
And his salary is Rs 1800 after 10 years.
$\Rightarrow {\text{X + 10R = 1800 - (2)}}$
Subtracting equation (1) from (2), we get
$\Rightarrow {\text{X + 10R - X - 4R = 1800 - 1500}} \\ \Rightarrow 6{\text{R = 300}} \\ \Rightarrow {\text{R = 50}} \\$
Putting the value of R in equation (2), we get
$\Rightarrow {\text{X + 10(50) = 1800}} \\ \Rightarrow {\text{X = 1800 - 500}} \\ \Rightarrow {\text{X = 1300}} \\$
So, the starting salary is Rs. 1300 and the yearly increment is Rs. 50.

Note:- There are two unknowns. To find two unknowns we require minimum two equations. And the equations can be solved by either the substitution method or the elimination method.