Question

A man starts his job with a certain monthly salary and a fixed increment every year. If
his salary will be Rs.11000 after 2 years and Rs.14000 after 4 years of his service. What is his
starting salary and what is the annual increment?
A. Starting salary is Rs.7500 and increment is Rs.2500
B. Starting salary is Rs.5000 and increment is Rs.1800
C. Starting salary is Rs.8000 and increment is Rs.1500
D. Starting salary is Rs.7000 and increment is Rs.1300

Answer 1

Hint: In this problem, first we have to consider the starting salary and the increment every year,
let $x$ and $y$ respectively. Since his salary after 2 years and the 4 years are given. From that

data we have to form the linear equations of $x$ and $y$.By solving the equations for $x$ and
$y$, which will gives the required amount of starting salary and increment.

Let starting salary $ = x$
Increment every year $ = y$
Therefore increment after 2 years and 4 years are $2y$ and $4y$ respectively.
Now, we can write the salary in terms of $x$ and $y$.
The salary after two years $ = x + 2y$ (1)
The salary after four years $ = x + 4y$ (2)

Given that salary after two year = Rs.11000 (3)
Salary after four year = Rs.14000 (4)

Equating equation (1) with equation (3),
$x + 2y = 11000$ (5)
Similarly, equating equation (2) with equation (4)
$x + 4y = 14000$ (6)

Subtracting equation (5) from equation (6) and solve these for the value of $x$ and $y$.
$\begin{array}{c}x + 4y - x - 2y = 14000 - 11000\\2y = 3000\\y = 1500\end{array}$
Thus, the increment per year is Rs.1500.

Substituting the value 1500 for $y$ in the equation (5), to find the value of x.
$\begin{array}{l}x + 2y = 11000\\ \Rightarrow x + 2 \times 1500 = 11000\\ \Rightarrow x +
3000 = 11000\\ \Rightarrow x = 11000 - 3000\\ \Rightarrow x = 8000\end{array}$
Thus, the starting salary is Rs.8000.

Hence, the correct option is C.

Note: Here, we have to determine the starting salary and the increment amount per year. We
have to calculate the salary after two years and four years with the considered value of starting
salary and increment. Since the salary after 2 years and the salary after 4 years are given. Thus,
by comparing the calculated expression with the given value we can easily find the starting
salary and the increment amount per year.