Harish started work at an annual salary of ₹ 5,00,000 and received an increment of ₹ 20,000 each year. After how many years did his income reach ₹ 7,00,000?                                                                                                        [Page No. 186]

Initial salary, $a = ₹ 5,00,000$

Yearly increment, $d = ₹ 20,000$

Required salary, $a_n = ₹ 7,00,000$

Using the $n^{\text{th}}$ term formula of A.P.:

$$a_n = a + (n - 1)d$$

Substitute the values:

$$7,00,000 = 5,00,000 + (n - 1)(20,000)$$

$$2,00,000 = (n - 1)(20,000)$$

$$10 = n - 1$$

$$n = 11$$

So, the $11^{\text{th}}$ year's salary is ₹ 7,00,000.

That means after 10 years of increments his income reaches ₹ 7,00,000.