Question

Read the following passage:

India is competitive manufacturing location due to the low cost of manpower and strong technical and engineering capabilities contributing to higher quality production runs. The production of TV sets in a factory increases uniformly by a fixed number every year. It produced 16000 sets in 6th year and 22600 in 9th year.

1. In which year, the production is 29,200 sets?
2. Find the production in the 8^th year.
   OR
   Find the production in first 3 years.
3. Find the difference of the production in 7^th year and 4^th year.

Answer 1

a₆ = 16000, a₉ = 22600

a + 5d = 16000  ...(1)

a + 8d = 22600  ...(2)

Substitute a = 1600 – 5d from (1)

16000 – 5d + 8d = 22600

3d = 22600 – 16000

3d = 6600

d = `6600/3` = 2200

a = 16000 – 5(2200)

a = 16000 – 11000

a = 5000

i. a_n = 29200, a = 5000, d = 2200

a_n = a + (n – 1)d

29200 = 5000 + (n – 1)2200

29200 – 5000 = 2200n – 2200

24200 + 2200 = 2200n

26400 = 2200n

n = `264/22`

n = 12

In 12^th year the production was Rs 29200

ii. n = 8, a = 5000, d = 2200

a_n = a + (n – 1) d

= 5000 + (8 – 1)2200

= 5000 + 7 × 2200

= 5000 + 15400

= 20400

The production during 8^th year is Rs 20400

OR

n = 3, a = 5000, d = 2200

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

= `3/2 [2(5000) + (3 - 1) 2200]`

S₃ = `3/2 (10000 + 2 xx 2200)`

= `3/2 (10000 + 4400)`

= 3 × 7200

= 21600

The production during first 3 years is 21600

iii. a₄ = a + 3d

= 5000 + 3(2200)

= 5000 + 6600

= 11600

a₇ = a + 6d

= 5000 + 6 × 2200

= 5000 + 13200

= 18200

a₇ – a₄ = 18200 – 11600 = 6600