The production of TV sets in a factory increases uniformly by a fixed number every year. It produced 8000 sets in 6th year, and 11300 in 9th year. Find the production in:
(i) first year
(ii) 8th year
(iii) total production in 6 years.

Question

The production of TV sets in a factory increases uniformly by a fixed number every year. It produced 8000 sets in 6th year, and 11300 in 9th year. Find the production in:
(i) first year
(ii) 8th year
(iii) total production in 6 years.

KnowledgeBoat · Accepted Answer

(i) Given, The production of TV sets in a factory increases uniformly by a fixed number every year. So the production is in A.P. Let the TV sets produced in first year be a and difference in production of each year be d. We know that, ∴ an = a + (n - 1)d Given, The sets produced in 6 years is 8000. ⇒ a + (6 - 1)d = 8000 ⇒ a + 5d = 8000 ....(1) The sets produced in the 9th year is 11300. ⇒ a + (9 - 1)d = 11300 ⇒ a + 8d = 11300 ....(2) Subtract Equation (1) from Equation (2), we get: ⇒ a + 8d - (a + 5d) = 11300 - 8000 ⇒ 3d = 3300 ⇒ d = ⇒ d = 1100. Substitute d = 1100 into Equation 1 : ⇒ a + 5(1100) = 8000 ⇒ a + 5500 = 8000 ⇒ a + 5500 = 8000 ⇒ a = 8000 - 5500 ⇒ a = 2500. Hence, the production in the first year is 2500 sets. (ii) Solving, ⇒ a8 = a + 7d = 2500 + 7(1100) = 2500 + 7700 = 10200. Hence, production in 8th year = 10200. (iii) Total production in 6 years : We know that, Sum of n terms of an A.P. is given by, ∴ Sn = [2a + (n - 1)d] ⇒ S6 = [2(2500) + (6 - 1)1100] = 3[5000 + (5)1100] = 3[5000 + 5500] = 3(10500) = 31500. Hence, total production in 6 years = 31500.

Mathematics

The production of TV sets in a factory increases uniformly by a fixed number every year. It produced 8000 sets in 6th year, and 11300 in 9th year. Find the production in:
(i) first year
(ii) 8th year
(iii) total production in 6 years.

AP

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Mathematics

The production of TV sets in a factory increases uniformly by a fixed number every year. It produced 8000 sets in 6th year, and 11300 in 9th year. Find the production in:(i) first year(ii) 8th year(iii) total production in 6 years.

AP

Related Questions

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The production of TV sets in a factory increases uniformly by a fixed number every year. It produced 8000 sets in 6th year, and 11300 in 9th year. Find the production in:
(i) first year
(ii) 8th year
(iii) total production in 6 years.