Question

Subba Rao started work in 1995 at an annual salary of Rs 5000 and received an increment of Rs 200 each year. After how many years did his income reach Rs 7000?

• A. 10
• B. 11
• C. 12
• D. 13

Answer 1

The correct option is B

11

Subba Rao's starting salary = Rs 5000

It means, first term = a = 5000

He gets an increment of Rs 200 after every year.

Therefore, common difference = d = 200

His salary after 1 year =5000 + 200 = Rs 5200

His salary after two years = 5200 + 200 = Rs 5400

Therefore, it is an AP of the form 5000, 5200, 5400, 5600... 7000.

We want to know in which year his incomes reach Rs 7000.

Using formula $a_n=a+(n-1)d$, to find $n^{th}$ term of arithmetic progression,, we can say that

$7000=5000+(n-1)\left(200\right)$

$\Rightarrow 7000=5000+200n-200$

$\Rightarrow 7000-5000+200=200n$

$\Rightarrow 2200=200n$

$\Rightarrow$ n = $\frac{2200}{200}$ = 11

It means after 11 years, Subba Rao's income would be Rs 7000.