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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?
Solution
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
d = 200
Let after nth year, his salary be Rs 7000.
Therefore, an = a + (n − 1) d
⇒ 7000 = 5000 + (n - 1) × 200
⇒ 7000 = 5000 + 200n - 200
⇒ 7000 = 4800 + 200n
⇒ 200n = 7000 - 4800
⇒ 200n = 2200
⇒ n = `2200/200`
⇒ n = 11
Therefore, in 11th year, his salary will be Rs 7000.
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