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If a shopkeeper sells an item 'A' at 20% profit and item 'B' at 25% profit, then the total profit made is ₹ 120. If he sells item 'A' at 25% profit and item 'B' at 20% profit, then the total profit made is ₹ 105. What is the sum of the cost price of items 'A' and 'B' ?
Explanation
Let the cost price of item A be x and item B be y.
Based on the profit percentages given, we can form the following linear equations:
1. 0.20x + 0.25y = 120
2. 0.25x + 0.20y = 105
To find the sum of the cost prices (x + y), we add the two equations together:
(0.20 + 0.25)x + (0.25 + 0.20)y = 120 + 105
0.45x + 0.45y = 225
Factoring out 0.45 from the left side:
0.45(x + y) = 225
Dividing both sides by 0.45:
x + y = 225 ÷ 0.45
x + y = 500
Thus, the sum of the cost price of items A and B is ₹ 500. Option C is correct.
SIMILAR QUESTIONS
A shopkeeper sells two items, A and B. Item B's cost price is twice as that of item A. The shopkeeper sells item A at 10% profit and item B at 20% profit. Which one of the following is the value of net profit?
A shopkeeper gives a discount of 10% on his items. ₹ 280 is the marked price of an item. On selling this item, the shopkeeper earns a profit of 26%. What is the cost price of the item ?