NCERT Class X Chapter 5: Arithmetic Progression Example 16(i)

NCERT Class X Chapter 5: Arithmetic Progression Example 16(i)

Question:

A manufacturer of TV sets produced 600 sets in the third year and 700 sets in the seventh year. Assuming that the production increases uniformly by a fixed number every year, find : the production in the 1st year

Given:

Production in the 3rd year = 600 sets
Production in the 7th year = 700 sets

To Find:

Production in the 1st year

Formula:

Let the production in the 1st year be 'a' and the uniform increase per year be 'd'.
Then the production in the nth year is given by: a + (n-1)d

Solution:

Production in the 3rd year: a + 2d = 600 ⇒ Equation 1

Production in the 7th year: a + 6d = 700 ⇒ Equation 2

Subtracting Equation 1 from Equation 2: (a + 6d) - (a + 2d) = 700 - 600 ⇒ 4d = 100 ⇒ d = 25

Substituting d = 25 in Equation 1: a + 2(25) = 600 ⇒ a + 50 = 600 ⇒ a = 550

Result:

Therefore, the production in the 1st year is 550 sets.

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