The ratio between marked price of article A to article B is 4 : 5 respectively. 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?

Let's solve the problem step by step:

Step 1: Let's assume the cost price of article A is 'x' and the cost price of article B is 'y'.

Step 2: The marked price of article A is 4 times the cost price, so the marked price of article A is 4x.

Step 3: The marked price of article B is 5 times the cost price, so the marked price of article B is 5y.

Step 4: The shopkeeper allowed a discount of d% on article A, so the selling price of article A becomes (100 - d)% of the marked price of article A, which is (100 - d)% of 4x.

Step 5: The shopkeeper allowed a discount of (d + 18)% on article B, so the selling price of article B becomes (100 - (d + 18))% of the marked price of article B, which is (100 - (d + 18))% of 5y.

Step 6: According to the given information, the selling price of both articles is equal. Therefore, we can equate the selling prices of article A and article B.

Step 7: (100 - d)% of 4x = (100 - (d + 18))% of 5y

Step 8: Simplifying the equation, we get: (100 - d)/100 * 4x = (100 - (d + 18))/100 * 5y

Step 9: Canceling out the common factors, we get: (100 - d) * 4x = (100 - (d + 18)) * 5y

Step 10: Expanding the equation, we get: 400x - 4dx = 500y - 5dy - 900y

Step 11: Simplifying further, we get: 400x - 4dx = -400y - 5dy

Step 12: Rearranging the terms, we get: 400x + 400y = -4dx - 5dy

Step 13: Dividing both sides by 4, we get: 100x + 100y = -dx - (5/4)dy

Step 14: According to the given information, the shopkeeper made a profit of 20% on article A and 25% on article B. Therefore, we can write the profit made on article A as 20% of the cost price of article A, which is 0.2x, and the profit made on article B as 25% of the cost price of article B, which is 0.25y.

Step 15: According to the given information, the profit made on article B is Rs. 384 more than that of article A. Therefore, we can write the equation: 0.25y - 0.2x = 384

Step 16: Now we have two equations: 100x + 100y = -dx - (5/4)dy 0.25y - 0.2x = 384

Step 17: We can solve these equations simultaneously to find the values of x and y, which represent the cost price of article A and article B, respectively.