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’ ?
According to the first condition:
20% profit on A + 25% profit on B = ₹ 120
0.20 * CA + 0.25 * CB = 120 (Equation 1)
According to the second condition:
25% profit on A + 20% profit on B = ₹ 105
0.25 * CA + 0.20 * CB = 105 (Equation 2)
We want to find the sum of the cost prices, which is CA + CB.
Adding Equation 1 and Equation 2:
(0.20 * CA + 0.25 * CA) + (0.25 * CB + 0.20 * CB) = 120 + 105
0.45 * CA + 0.45 * CB = 225
0.45 * (CA + CB) = 225
Now, solve for CA + CB:
CA + CB = 225 / 0.45
CA + CB = 225 / (45/100)
CA + CB = 225 * (100/45)
CA + CB = (225/45) * 100
CA + CB = 5 * 100
CA + CB = 500
The sum of the cost price of items ‘A’ and ‘B’ is ₹ 500.
20 CA + 25 CB = 12000
25 CA + 20 CB = 10500
Adding these yields 45(CA + CB) = 22500, leading to CA + CB = 500.