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.