Question

A person got a job with a fixed salary and a certain yearly increment. After 2 year his salary was Rs.10,000 and after 4 years it was Rs.15,000. Find his salary after 10 years.
(a) Rs.32,500
(b) Rs.27,500
(c) Rs.27,250
(d) Rs.30,000

Answer 1

Hint: Take the initial salary and yearly increment as x and y. Now find 2 equations containing variable x and y with the given conditions. Solve for x and y. Now find the salary after 10 years, knowing the initial salary and yearly increments.

Complete step-by-step answer:
Let us consider his fixed salary as ‘x’. Let us consider the yearly increment of the man as ‘y’. It is said that after 2 years his salary is Rs.10,000.
To formulate the expression, we need his salary at the start of the job with yearly increment. Thus after 2 years of service,
\[x+2y=10000\] - (1)
Now after 4 year of service his salary is Rs.15,000. We can formulate it as,
\[x+4y=15000\] - (2)
Let us solve both the expressions (1) and (2). For that subtract (1) from (2).
\[x+4y=15000\]
\[x+2y=10000\]
 (-) (-) (-)
\[2y=5000\]
\[\therefore y=2500\]
Thus we got the yearly increment as Rs.2500. Now put this value of y in (1).
\[\begin{align}
  & x+\left( 2\times 2500 \right)=10000 \\
 & \Rightarrow x=10000-5000=5000 \\
\end{align}\]
Hence the starting salary of the man is Rs.5000.
Now we need to find the salary of the man after 10 years. Including the starting salary and yearly increments i.e. \[x+10y\]
\[\begin{align}
  & x+10y=5000+10\times 2500 \\
 & x+10y=5000+25000 \\
\end{align}\]
\[x+10y\] = Rs.30,000
Thus we got the salary of the person after 10 years as Rs.30,000.
\[\therefore \] Option (d) is the correct answer.

Note: You can find the salary of the man for any year if you know the initial salary and yearly increments of the man. Hence our main aim in this question is to calculate the value of x and y. If you want the salary of a man after 20 year then, \[\left( x+20y \right)\] will give the answer.