NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.2 Question 19

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.2 Question 19

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?

Given:

Starting salary in 1995 = Rs 5000
Annual increment = Rs 200

To Find:

The year in which his income reached Rs 7000.

Formula:

nth term of an AP = a + (n-1)d, where 

'a' is the first term and 

'd' is the common difference.

Solution:

Let a = 5000

d = 200 and 

The salary forms an AP: 5000, 5200, 5400, ....... 

an = 7000

Substituting an= 7000, a = 5000 and d = 200 in nth term of an AP formula we have

7000 = 5000 + (n - 1) 200

⇒ n - 1 = 7000 - 5000 200  

⇒ n - 1 = 7000 - 5000 200  

⇒ n - 1 = 2000 200

⇒ n - 1 =10

⇒ n = 10 + 1

⇒ n = 11

Therefore, his income reached Rs 7000 in 11th years.

Result:

Subba Rao's income reached Rs 7000 in the 11th year. ( 2005 )

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