Question

Subba Rao started work in $1995$ at an annual salary of Rs. $5000$ and received an increment of Rs. $200$ each year. In which year did his income reach Rs. $7000$

Answer 1

It can be observed that the incomes that Subba Rao obtained in various years are in A.P. as every year, his salary is increased by Rs $200$.

Therefore, the salaries of each year after $1995$ are

$5000,5200,5400,\dots$

Here, $a=5000$

$d=200$

Let after $n^{th}$ year, his salary be Rs $7000$.

Therefore, $a_n=a+(n-1)d$

$\Rightarrow 7000=5000+(n-1)200$

$\Rightarrow 200(n-1)=2000$

$\Rightarrow (n-1)=10$

$\therefore n=11$

Therefore, in ${11}^{th}$ year, his salary will be Rs $7000$.