Question

In the month of April to June 2022, the exports of passenger cars from India increased by 26% in the corresponding quarter of 2021-22, as per a report. A car manufacturing company planned to produce 1800 cars in 4th year and 2600 cars in 8th year. Assuming that the production increases uniformly by a fixed number every year.

Based on the above information answer the following questions.

1. Find the production in the 1^st year
2. Find the production in the 12^th year.
3. Find the total production in first 10 years.
   [OR]
   In how many years will the total production reach 31200 cars?

Answer 1

I. Since the production increases uniformly by a fixed number every year, the number of cars manufactured in 1^st, 2^nd, 3^rd, ...., years will form an AP.

So, a + 3d = 1800 and a + 7d = 2600

So d = 200 and a = 1200

II. t₁₂ = a + 11d

⇒ t₃₀ = 1200 + 11 × 200

⇒ t₁₂ = 3400

III. S_n = `n/2 [2a + (n - 1)d]`

⇒ S₁₀ = `10/2 [2 xx 1200 + (10 - 1) 200]`

⇒ S₁₀ = `13/2 [2 xx 1200 + 9 xx 200]`

⇒ S₁₀ = 5 × [2400 + 1800]

⇒ S₁₀ = 5 × 4200

⇒ S₁₀ = 21000

[OR]

Let in n years the production will reach to 31200.

S_n = `n/2 [2a + (n - 1)d]` = 31200

⇒ `n/2 [2 xx 1200 + (n - 1)200]` = 31200

⇒ n[12 + (n – 1)] = 312

⇒ n₂ + 11n – 312 = 0

⇒ n₂ + 24n – 13n – 312 = 0

⇒ (n + 24) (n – 13) = 0

⇒ n = 13 or – 24

As n can’t be negative.

So n = 13