Question

Jaydeep starts his job with a certain monthly salary and earns a fixed increment in his monthly salary at the middle of every year starting from the first year. If his monthly salary was Rs. $78000$ at the end of $6$ years of service and Rs. $84000$ at the end of $12$ years of service, find his initial salary (in Rs.).

• A. $64000$
• B. $72000$
• C. $84000$
• D. $92000$

Answer 1

The correct option is B $72000$

Let initial monthly salary be Rs. $x$ and increment be Rs. $y$.

Therefore, salary of first $6$ months $=$ Rs. $x$

Salary of next $1$ year $=$ Rs. $12(x+y)$.

Salary of next $1$ year $=12(x+2y)$

Again, salary for next $1$ year $=12(x+5y)$

Therefore, salary of last $6$ months $=6(x+6y)$

Monthly salary of last month $=x+6y$

$\Rightarrow x+6y=78000$ ....(1)

Similarly, salary at the end of $12$ years is $x+12y$.

$\Rightarrow x+12y=84000$ ....(2)

Subtracting equations (1) and (2), we get

$6y=6000$

$\Rightarrow y=1000$

Put this value in equation (1), we get

$x+6\left(1000\right)=78000$

$\Rightarrow x=78000-6000$

$\Rightarrow y=72000$

Thus, monthly salary is Rs. $72000$ and annual increment is Rs. $1000$.