A shopkeeper increase price by 40% and give discount of 40% but measure 15%less.find loss and gain

To solve this problem, we need to break it down into parts:

1. **Price Increase and Discount:**

   Let's assume the original price of the item is \( P \).

   - After a 40% increase, the new price becomes \( P \times 1.40 \).
   - Then, a 40% discount is applied to the increased price, making the final price \( (P \times 1.40) \times 0.60 = P \times 0.84 \).

   So, after increasing the price by 40% and then giving a 40% discount, the effective price becomes 84% of the original price \( P \).

2. **Measuring 15% Less:**

   When the shopkeeper measures 15% less, it means they are giving only 85% of the actual quantity.

   If the original quantity is \( Q \), the given quantity is \( Q \times 0.85 \).

3. **Finding Loss or Gain:**

   Now, let's determine the effective cost per unit for the shopkeeper and the customer:

   - **Shopkeeper's perspective:** They sell \( Q \times 0.85 \) quantity at the price of \( P \times 0.84 \).
   - The effective price per unit for the shopkeeper is \( \frac{P \times 0.84}{Q \times 0.85} = \frac{0.84P}{0.85Q} \).

   Simplifying this, we get:

   \[
   \frac{0.84P}{0.85Q} = \frac{84P}{85Q}
   \]

   - The original price per unit was \( \frac{P}{Q} \).

   To find the percentage loss or gain:

   \[
   \text{Effective price per unit} = \frac{84}{85} \times \frac{P}{Q}
   \]

   - Comparing this to the original price per unit \( \frac{P}{Q} \):

   \[
   \text{Loss/Gain Percentage} = \left(1 - \frac{84}{85}\right) \times 100\%
   \]

   Simplifying this:

   \[
   \text{Loss/Gain Percentage} = \left(1 - 0.9882\right) \times 100\% = 1.1765\% \text{ loss}
   \]

Thus, the shopkeeper experiences approximately a 1.18% loss.

Would you like further details or have any questions? Here are some more questions you can ask:

1. How would the calculations change if the discount was 30% instead of 40%?
2. What if the shopkeeper measures 10% less instead of 15%?
3. How does changing the percentage of price increase affect the overall loss/gain?
4. Can you explain how the price increase and discount interact mathematically?
5. How do these types of pricing strategies affect consumer perception?

**Tip:** When dealing with percentage changes, remember that sequential percentage increases and decreases do not simply cancel each other out.

Learn how to calculate profit and loss when a shopkeeper increases prices by 40% and then applies a 40% discount, while also measuring 15% less of the product. Understand the interaction of percentage changes in pricing and quantity measurements.

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