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

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2005

2002

2004

2007

answer is A.

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Detailed Solution

We are given that the initial salary in the year 1995 as Rs.5000
Let us assume that the first salary as
⇒ a = 5000
We are given that there is an increment of Rs.200 every year.
Here, we can see that the salary increment gives the form of A.P
We know that the general representation of A.P is given as
a, a + d, a + 2d,.....
Where a is the first term and d is the common term.
Let us assume that the given increment as
⇒d=200
We are asked to find the year at which the salary becomes Rs.7000
Let us assume that the final amount as

⇒ T n = 7000

We know that the formula

n t h

term of an A.P as

⇒ T n = a + (n − 1) d

By using the above formula to given information then we get
⇒7000 = 5000 + (n − 1)200
⇒2000 = (n − 1)200
⇒n – 1 = 10
⇒n = 11
Therefore, we can say that at the end of

11 t h

year form 1995 the salary becomes Rs.7000
We know that the year after r years from n is given as n + r − 1
Let us add 11 to 1996 by using the above condition then we get
⇒ 1995 + 11 – 1 = 2005
Therefore, we can conclude that in the year 2005 the salary becomes Rs.7000

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