Question : Prakash bought 2 items, paying the same price for each of them. He sold one item at a profit of 20% and the other item at a profit of 25%. What is the overall percentage profit he made?

Option 1: 37.5%

Option 2: 24.5%

Option 3: 16.5%

Option 4: 22.5%

Correct Answer: 22.5%

Solution : Let the cost price of each item be denoted as "C".
Let the selling price of the first item be denoted as "S1", and its profit percentage be denoted as "P1".
Let the selling price of the second item be denoted as "S2", and its profit percentage be denoted as "P2".
The total cost price of the two items is 2C, and the total selling price is S1 + S2.
Prakash sold one item at a profit of 20%, so we have:
P1 = 20%
S1 = $\text{C} + (\frac{\text{P1}}{100}) \times \text{C}$
S1 = $\text{C} + (\frac{20}{100}) \times \text{C}$ = 1.2C
Prakash sold the other item at a profit of 25%, so we have:
P2 = 25%
S2 = $\text{C} + (\frac{\text{P2}}{100}) \times \text{C}$
S2 = $\text{C} + (\frac{25}{100}) \times \text{C}$ = 1.25C
Total cost Price = 2C
Total selling Price = S1 + S2 = 1.2C + 1.25C = 2.45C
The overall percentage profit = $[\frac{(\text{Total selling price} - \text{Total cost price}) }{\text{Total cost price}}] × 100$
Substituting the values, we get:
= $[\frac{(2.45\text{C} - 2\text{C}) }{2\text{C}}] × 100$
= $(\frac{0.45\text{C}}{2\text{C}}) × 100$
= 22.5%
Hence, the correct answer is 22.5%.