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:
\(5000, 5200, 5400, ……\)
Here,
\(a = 5000\) and \(d = 200\)
Let after \(n^{th}\) year, his salary be Rs. \(7000\).
Therefore,
\(a_n = a + (n − 1) d\)
\(7000 = 5000 + (n − 1) 200\)
\(200(n − 1) = 2000\)
\((n − 1) = 10\)
\(n = 11\)

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