Explanation:

- Let radio's cost price = Rs R, TV's cost price = Rs T.

- First sale:

25% profit on radio ? Sale price = R × 1.25

10% profit on TV ? Sale price = T × 1.10

Total sale price = Rs 30,400

So, 1.25R + 1.10T = 30,400

- Second sale:

10% profit on radio ? Sale price = R × 1.10

25% profit on TV ? Sale price = T × 1.25

Total sale price = Rs 30,700

So, 1.10R + 1.25T = 30,700

- Now, solving these equations:

1. 1.25R + 1.10T = 30,400

2. 1.10R + 1.25T = 30,700

Add both:

1.25R + 1.10T + 1.10R + 1.25T = 30,400 + 30,700

2.35R + 2.35T = 61,100

R + T = 61,100 / 2.35 = 26,000

Subtract (2 from 1):

(1.25R + 1.10T) - (1.10R + 1.25T) = 30,400 - 30,700

(0.15R - 0.15T) = -300

0.15(R - T) = -300

R - T = -300 / 0.15 = -2,000

R = T - 2,000

Substitute into R + T = 26,000:

(T - 2,000) + T = 26,000

2T = 28,000

T = 14,000

R = 14,000 - 2,000 = 12,000

- So, the cost price of the radio is Rs 12,000.

- Option Check:

1. Rs 10,000 — Not correct

2. Rs 12,000 — Correct

3. Rs 8,000 — Not correct

4. Rs 9,000 — Not correct

Correct Answer: Option 2: Rs 12,000