Both Vikash and Vijay sold an article at a profit of 20\% on the selling price. The average cost price of the articles for Vikash and Vijay is Rs.700. The profit earned by Vikash is Rs.50 less than the profit earned by Vijay. What is the average selling price of the articles for Vikash and Vijay?

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Accepted Answer

**Solution:**

1. Let the selling prices of Vikash and Vijay be $ S_V $ and $ S_J $ respectively.

2. Given that both sold at 20\% profit on selling price, which means:
   $$
   \text{Profit} = 20\% \times \text{Selling Price} = 0.2 \times S
   $$

3. Let the cost prices be $ C_V $ and $ C_J $ for Vikash and Vijay respectively.

4. Profit is also $ \text{Selling Price} - \text{Cost Price} $, so:
   $$
   S_V - C_V = 0.2 S_V \implies C_V = S_V - 0.2 S_V = 0.8 S_V
   $$
   Similarly,
   $$
   C_J = 0.8 S_J
   $$

5. The average cost price is given as Rs.700:
   $$
   \frac{C_V + C_J}{2} = 700 \implies C_V + C_J = 1400
   $$

6. Substitute $ C_V = 0.8 S_V $ and $ C_J = 0.8 S_J $:
   $$
   0.8 S_V + 0.8 S_J = 1400 \implies 0.8 (S_V + S_J) = 1400 \implies S_V + S_J = \frac{1400}{0.8} = 1750
   $$

7. Profit of Vikash is Rs.50 less than Vijay's profit:
   $$
   (S_V - C_V) = (S_J - C_J) - 50
   $$
   Using $ C_V = 0.8 S_V $ and $ C_J = 0.8 S_J $:
   $$
   S_V - 0.8 S_V = S_J - 0.8 S_J - 50 \implies 0.2 S_V = 0.2 S_J - 50
   $$
   Multiply both sides by 5:
   $$
   S_V = S_J - 250
   $$

8. From step 6, $ S_V + S_J = 1750 $, substitute $ S_V = S_J - 250 $:
   $$
   (S_J - 250) + S_J = 1750 \implies 2 S_J = 2000 \implies S_J = 1000
   $$

9. Then, $ S_V = 1000 - 250 = 750 $

10. Average selling price:
    $$
    \frac{S_V + S_J}{2} = \frac{750 + 1000}{2} = \frac{1750}{2} = 875
    $$

**Answer:** Rs. 875

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