The cost price of a TV is Rs. 1800 more than the cost price of a mixer. The TV is sold at a 20\% profit, and the mixer is sold at a 15\% profit. If the difference between their selling prices is Rs. 2860, what is the cost price of the TV?

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**Solution:**

1. Let the cost price of the mixer be $ x $ rupees.

2. Then, the cost price of the TV is $ x + 1800 $ rupees.

3. Selling price of the TV = Cost price + 20\% profit = $$ (x + 1800) \times 1.20 = 1.20x + 2160$ $

4. Selling price of the mixer = Cost price + 15\% profit = $$ x \times 1.15 = 1.15x $$

5. According to the problem, the difference between the selling prices is Rs. 2860:
   $$
   (1.20x + 2160) - 1.15x = 2860
   $$

6. Simplify the equation:
   $$
  $ 1.20x - 1.15x + 2160 = 2860 \
   0.05x + 2160 = 2860 \
   0.05x = 2860 - 2160 = 700 \
   x = \frac{700}{0.05} = 14000$
   $$

7. Cost price of the TV = $ x + 1800 = 14000 + 1800 = 15800 $

**Answer:** Rs. 15800

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