A shopkeeper increase price by 40% and give discount of 40% but measure 850gram instead of 1kg .find loss and gain

Let's break down the problem step by step to find the loss or gain:

1. **Price Increase and Discount:**

   Let's assume the original price of 1 kg of the product 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 850 grams instead of 1 kg:**

   The shopkeeper gives 850 grams instead of 1 kg, which means the customer receives only 85% of the quantity they pay for.

3. **Finding Loss or Gain:**

   To determine the effective price per unit for the shopkeeper and the customer:

   - **Shopkeeper's perspective:** They sell 850 grams (0.85 kg) at the price of 1 kg (P \times 0.84).
   - The effective price per kg for the shopkeeper is:

     \[
     \text{Effective Price per kg} = \frac{P \times 0.84}{0.85 \, \text{kg}} = \frac{0.84P}{0.85}
     \]

   Simplifying this, we get:

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

   - The original price per kg was \( P \).

   To find the percentage loss or gain:

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

   - Comparing this to the original price per kg \( P \):

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

   Simplifying this:

     \[
     \text{Loss/Gain Percentage} = \left(1 - \frac{84}{85}\right) \times 100\% = \left(1 - 0.9882\right) \times 100\% = 1.1765\% \text{ loss}
     \]

So, 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 900 grams instead of 850 grams?
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.

Understand how a shopkeeper's pricing strategy affects profit and loss. Learn step-by-step calculations involving a 40% price increase followed by a 40% discount, and selling 850 grams instead of 1 kg. Find out about the 1.18% loss incurred and explore related scenarios.

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