Milk was bought for 150. For what price should it be sold to gain 20% profit?

Question

Accepted Answer

To determine the selling price of the milk to achieve a 20% profit, we start by understanding the concept of profit percentage. Profit percentage is calculated based on the cost price, and it indicates how much profit is made relative to the cost price.

1. **Calculate the Profit Amount:**
   - The cost price of the milk is ₹150.
   - The desired profit percentage is 20%.
   - Profit is calculated as: 
     $$
     \text{Profit} = \left(\frac{\text{Profit Percentage}}{100}\right) \times \text{Cost Price}
     $$
   - Substituting the given values:
     $$
     \text{Profit} = \left(\frac{20}{100}\right) \times 150 = 0.2 \times 150 = ₹30
     $$

2. **Calculate the Selling Price:**
   - The selling price is the sum of the cost price and the profit.
   - Selling Price = Cost Price + Profit
   - Substituting the values:
     $$
     \text{Selling Price} = 150 + 30 = ₹180
     $$

Therefore, to achieve a 20% profit, the milk should be sold for ₹180, which corresponds to Option 2.

**Explanation of Why Other Options are Incorrect:**

- **Option 1: ₹170**
  - If the selling price were ₹170, the profit would be:
    $$
    \text{Profit} = 170 - 150 = ₹20
    $$
  - The profit percentage would then be:
    $$
    \text{Profit Percentage} = \left(\frac{20}{150}\right) \times 100 = 13.33\%
    $$
  - This is less than the required 20% profit, making Option 1 incorrect.

- **Option 3: ₹130**
  - If the selling price were ₹130, it would actually result in a loss:
    $$
    \text{Loss} = 150 - 130 = ₹20
    $$
  - This is not a profit, hence Option 3 is incorrect.

- **Option 4: ₹120**
  - If the selling price were ₹120, it would also result in a loss:
    $$
    \text{Loss} = 150 - 120 = ₹30
    $$
  - This is not a profit, making Option 4 incorrect.

In conclusion, Option 2 (₹180) is the correct answer as it ensures a 20% profit on the cost price of ₹150.