Question

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

NCERT Class X
Mathematics - Mathematics

Chapter _ARITHMETIC PROGRESSIONS

Answer 1

Let Subba's salary be increased to Rs. 7000 after x years

So, 200x = 7000-5000
or, x = 2000/200 = 10

So, income will become Rs. 7000 in (1995+10) = in 2005

Answer 2

Annual salary in 1st Year = 5000

Salary in 2nd year = 5200

Salary in 3rd year = 5400

Thus we get an AP

5000, 5200, 5400

a = 5000

d = t2 - t1

= 5200 - 5000

= 200

Let the salary reach 7000 in nth year

an = a + (n - 1) × d

7000 = 5000 + (n - 1) × 200

7000 - 5000 = (n - 1) × 200

2000 = (n - 1) × 200

2000 ÷ 200 = (n - 1)

10 = (n - 1)

11 = n

His income will reach 7000 in 11th year