The cost price of article A is 80\% of the cost price of article B. Article A is marked 60\% above its cost price, and a discount of 20\% is given on the marked price. If the discount allowed on article A is Rs. 20 more than the profit earned on article A, what is the cost price of article B?

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Accepted Answer

**Solution:**

1. Let the cost price of article B be $ x $.

2. Then, the cost price of article A is 80\% of $ x $, i.e.,
   $$
   $\text{CP}_A $= 0.8x
   $$

3. The marked price (MP) of article A is 60\% above its cost price:
   $$
   $\text{MP}_A = \text{CP}_A + 0.6 \times \text{CP}_A = 1.6 \times 0.8x = 1.28x$
   $$

4. A discount of 20\% is given on the marked price, so the selling price (SP) of article A is:
   $$
   $\text{SP}_A = \text{MP}_A - 0.2 \times \text{MP}_A = 0.8 \times 1.28x = 1.024x$
   $$

5. The discount allowed on article A is:
   $$
   $\text{Discount} = \text{MP}_A - \text{SP}_A = 1.28x - 1.024x = 0.256x$
   $$

6. The profit earned on article A is:
   $$
   $\text{Profit} = \text{SP}_A - \text{CP}_A = 1.024x - 0.8x = 0.224x$
   $$

7. According to the problem, the discount is Rs. 20 more than the profit:
   $$
   0.256x = 0.224x + 20
   $$

8. Simplify the equation:
   $$
   $0.256x - 0.224x = 20 \ 0.032x = 20 \ x = \frac{20}{0.032} = 625$
   $$

**Answer:** Rs. 625

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