A person got 20% profit by selling 20 items in 60 rupees. How much items did he buy in 60 rupees?

Question

Accepted Answer

To determine how many items the person bought for 60 rupees, given that they sold 20 items for 60 rupees and made a 20% profit, we need to follow these steps:

1. **Understanding the Profit Calculation:**
   - The person sold 20 items for 60 rupees and made a 20% profit.
   - This means the selling price (SP) is 120% of the cost price (CP).

2. **Calculate the Cost Price (CP) of 20 Items:**
   - Let the cost price of 20 items be $ x $.
   - Since the selling price is 120% of the cost price, we have:
     $$
     1.2x = 60
     $$
   - Solving for $ x $:
     $$
     x = \frac{60}{1.2} = 50
     $$
   - Therefore, the cost price of 20 items is 50 rupees.

3. **Determine the Number of Items Bought for 60 Rupees:**
   - If 20 items cost 50 rupees, we need to find out how many items can be bought for 60 rupees.
   - The cost per item is:
     $$
     \text{Cost per item} = \frac{50}{20} = 2.5 \text{ rupees per item}
     $$
   - For 60 rupees, the number of items bought is:
     $$
     \text{Number of items} = \frac{60}{2.5} = 24
     $$

Thus, the person bought 24 items for 60 rupees, which corresponds to Option 2.

**Explanation for Incorrect Options:**

- **Option 1 (22 items):** If the person bought 22 items for 60 rupees, the cost per item would be approximately 2.73 rupees, which does not align with the calculated cost per item of 2.5 rupees.

- **Option 3 (25 items):** If the person bought 25 items for 60 rupees, the cost per item would be 2.4 rupees, which is less than the calculated cost per item of 2.5 rupees.

- **Option 4 (26 items):** If the person bought 26 items for 60 rupees, the cost per item would be approximately 2.31 rupees, which is also less than the calculated cost per item of 2.5 rupees.

Therefore, Option 2 is the only correct answer, as it accurately reflects the number of items that could be bought for 60 rupees based on the given profit scenario.