Question:medium

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?

Updated On: Jan 13, 2026
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Solution and Explanation

Subba Rao's incomes in various years form an arithmetic progression (A.P.) with an annual increment of Rs. \(200\). The salaries from 1995 onwards are: \(5000, 5200, 5400, ……\). Here, the first term is \(a = 5000\) and the common difference is \(d = 200\). If Subba Rao's salary reaches Rs. \(7000\) in the \(n^{th}\) year, we use the formula \(a_n = a + (n − 1) d\). Substituting the values: \(7000 = 5000 + (n − 1) 200\). This simplifies to \(200(n − 1) = 2000\), leading to \((n − 1) = 10\) and thus \(n = 11\).

Therefore, Subba Rao's salary will be Rs. \(7000\) in the \(11^{th}\) year.

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