Question

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. The production of the TV sets during the first year was:

(a) 4000
(b) 4500
(c) 5000
(d) 5500

2. What was the uniform increase in the production of TV sets every year?

(a) 1800
(b) 2400
(c) 1600
(d) 2200 

3. The production of the TV sets during the 8th year was:

 (a) 20000
(b) 20400
(c) 21200
(d) 22800

4. The total production of the TV sets during first 6 years was:

(a) 56000
(b) 72000
(c) 66000
(d) 63000 

5. The average production of the TV sets during first 6 years was: 

(a) 10500
(b) 11000
(c) 11500
(d) 12000

Answer 1

1. The correct option is (c).

Reasoning:

Let the first year production be \[a\] and uniform increase be \[d\].

Given: \[a_6 = a + 5d = 16000\] and \[a_9 = a + 8d = 22600\].

Subtracting gives \[3d = 6600 \implies d = 2200\].

Thus, \[a = 16000 - 5(2200) = 16000 - 11000 = 5000\].

Options (a), (b) and (d) are incorrect calculations of the initial term \[a\].

2. The correct option is (d).

Reasoning:

From \[a_9 - a_6 = (a + 8d) - (a + 5d) = 3d\], we have \[22600 - 16000 = 6600\].

Therefore, \[d = \frac{6600}{3} = 2200\].

Options (a), (b) and (c) represent incorrect division or arithmetic errors.

3. The correct option is (b).

Reasoning:

The production in the 8th year is \[a_8 = a_9 - d = 22600 - 2200 = 20400\] (or \[a + 7d = 5000 + 7 \times 2200 = 20400\]).

Option (a) subtracts incorrectly, (c) adds incorrectly, and (d) exceeds the 9th year's production.

4. The correct option is (d).

Reasoning:

Using the sum formula \[S_n = \frac{n}{2}(a + a_n)\] for \[n = 6\]: \[S_6 = \frac{6}{2}(a + a_6) = 3(5000 + 16000) = 3 \times 21000 = 63000\]

Options (a), (b) and (c) do not equal the computed product of \[3 \times 21000\].

5. The correct option is (a).

Reasoning:

The average production during the first 6 years is \[\frac{S_6}{6} = \frac{63000}{6} = 10500\] sets.

Options (b), (c) and (d) are incorrect values resulting from calculation errors.