If a shopkeeper sells an item ‘A’ at 20% profit and item ‘B’ at 25% pr

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’ ?

₹ 300
₹ 400
₹ 500
₹ 600
This question was previously asked in
UPSC CISF-AC-EXE – 2021
The correct answer is ₹ 500.
Let the cost price of item ‘A’ be CA and the cost price of item ‘B’ be CB.
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.

This problem can also be solved by multiplying the equations to remove decimals first and then adding them, or by using substitution or elimination methods to find CA and CB individually before summing them. For instance, multiplying equations by 100 gives:
20 CA + 25 CB = 12000
25 CA + 20 CB = 10500
Adding these yields 45(CA + CB) = 22500, leading to CA + CB = 500.
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