A shopkeeper cheats to the extent of 10% while buying as well as selling,by using false weighs,his total gain?

When a shopkeeper cheats by using false weights, both while buying and selling, he gains a profit in two steps. Let's break it down:

1. **First gain (buying):** The shopkeeper cheats by getting 10% more goods while buying. So if the cost price is \( C \), the shopkeeper effectively gets goods worth \( 1.1C \) but still pays \( C \), resulting in an effective buying gain of 10%.

2. **Second gain (selling):** The shopkeeper also cheats by selling 10% less than the actual weight. So, if the marked price is \( S \), the shopkeeper only delivers 90% of the goods, while receiving the full selling price.

### Calculating total gain:

The shopkeeper makes a 10% profit twice. This can be modeled as follows:

- If the cost price is \( C \), after the first cheating act, the effective value of goods the shopkeeper has is \( 1.1C \).
- After the second act of cheating, by selling less, the shopkeeper gains an additional 10%, so the total gain is compounded:

\[
\text{Total Gain} = (1.1) \times (1.1) = 1.21
\]

Thus, the shopkeeper's total gain is 21%. This means the shopkeeper makes a 21% profit by cheating 10% while buying and 10% while selling.

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Would you like further details or have any questions?

Here are five questions you could explore:

1. How does compounding affect percentages in real-life transactions?
2. What would happen if the cheating percentage was 20% instead of 10%?
3. How can shopkeepers be caught for such malpractices?
4. What is the mathematical formula for successive percentage gain or loss?
5. How is cheating through false weights illegal in trade?

**Tip:** Successive percentage changes multiply, so the total percentage gain or loss is not simply additive, it's a compounded effect!

A shopkeeper cheats to the extent of 10% while buying as well as selling, by using false weights. What is his total gain?

Discover how to calculate the total profit a shopkeeper makes by cheating with false weights while buying and selling. This problem involves understanding successive percentage gains, the compounding effect, and applying percentage formulas. Perfect for students in Grades 8-10.

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