Question

Suba Rao started work in $1995$ at an annual salary of $Rs.5000$ and received a $Rs.200$ raise each year. In what year did his annual salary will reach $Rs.7000$?

Answer 1

Annual salary received by Suba Rao in $1995,1997,1999,...$ is
$Rs.5000,Rs.5200,Rs.5400,...$

Clearly, it is an arithmetic progression with first term $a=5000$ and common difference $d=200$.
Suppose Suba Rao's annual salary reaches to $Rs.7000$ in $n^{th}$ years.

Then, $n^{th}$ term of the above A.P. $=7000$
$⟹a+(n-1)d=7000$$⟹5000+(n-1)\times 200=7000$

$⟹(n-1)\times 200=2000$
$⟹n-1=\frac{2000}{200}⟹n-1=10⟹n=11$
Thus, ${11}^{th}$ annual salary received by Suba Rao will be $Rs.7000$. This means that after $10$ years i.e., in the year $2005$ his annual salary will reach to $Rs.7000$.