Ratio between marked price of article A to article B is $4 : 5$. Shopkeeper allowed $d\%$ discount on article A and $(d + 18)\%$ discount on article B, so selling price of both articles become equal. If shopkeeper made a profit of $20\%$ on article A and $25\%$ on article B and profit made on article B is Rs. 384 more than that of article A, then find the cost price of article A and article B respectively.

Question

Accepted Answer

**Solution:**

1. Let the marked price of article A be $400x$ and article B be $500x$ (since ratio is $4:5$).

2. Given discounts: $d\%$ on A and $(d + 18)\%$ on B.

3. Selling prices are equal:
   $$
   400x \times \frac{100 - d}{100} = 500x \times \frac{100 - (d + 18)}{100}
   $$

4. Simplify:
   $$
   400(100 - d) = 500(82 - d) \quad \Rightarrow \quad 40000 - 400d = 41000 - 500d
   $$

5. Rearranging:
   $$
   500d - 400d = 41000 - 40000 \Rightarrow 100d = 1000 \Rightarrow d = 10\%
   $$

6. Cost price of article A (with 20% profit):
   $$
   \text{Selling Price of A} = 400x \times \frac{90}{100} = 360x
   $$
   Since profit is 20%,
   $$
   \text{Cost Price of A} = \frac{360x \times 100}{120} = 300x
   $$

7. Cost price of article B (with 25% profit):
   Selling price of B:
   $$
   500x \times \frac{72}{100} = 360x
   $$
   Since profit is 25%,
   $$
   \text{Cost Price of B} = \frac{360x \times 100}{125} = 288x
   $$

8. Profit difference given:
   $$
   \text{Profit on B} - \text{Profit on A} = 384
   $$
   Profit on A:
   $$
   360x - 300x = 60x
   $$
   Profit on B:
   $$
   360x - 288x = 72x
   $$

9. So,
   $$
   72x - 60x = 384 \Rightarrow 12x = 384 \Rightarrow x = 32
   $$

10. Calculate cost prices:
    $$
    \text{Cost Price of A} = 300x = 300 \times 32 = 9600 \text{ Rs}
    $$
    $$
    \text{Cost Price of B} = 288x = 288 \times 32 = 9216 \text{ Rs}
    $$

**Answer:** 9600 Rs. and 9216 Rs.

Answer

Answer

Answer