a wholesale vegetable vendor sold potatoes marked at rs 1000. four successive discounts of 10% each instead of the promised 40% discount. by what amount did the vendor defraud the customer (a) 58.10 rupees (b) 56.10 rupees (c) 65.10 rupees (d) 66.10 rupees

Let's solve this problem step by step.

1. **Original Marked Price**: The potatoes are marked at Rs 1000.

2. **Discounted Price with 40% Discount**: 
   \[
   \text{Price after 40% discount} = 1000 \times \left(1 - \frac{40}{100}\right) = 1000 \times 0.6 = 600 \text{ rupees}
   \]
   
3. **Price after Four Successive 10% Discounts**: 

   After the first 10% discount:
   \[
   1000 \times \left(1 - \frac{10}{100}\right) = 1000 \times 0.9 = 900 \text{ rupees}
   \]
   
   After the second 10% discount:
   \[
   900 \times 0.9 = 810 \text{ rupees}
   \]
   
   After the third 10% discount:
   \[
   810 \times 0.9 = 729 \text{ rupees}
   \]
   
   After the fourth 10% discount:
   \[
   729 \times 0.9 = 656.1 \text{ rupees}
   \]

4. **Difference in Price**:
   \[
   \text{Difference} = 656.1 - 600 = 56.1 \text{ rupees}
   \]

So, the vendor defrauded the customer by **Rs 56.10**. 

Thus, the correct answer is **(b) 56.10 rupees**.

Would you like more details, or do you have any questions?

Here are 5 related questions to expand your understanding:

1. How would the fraud amount change if the vendor offered three successive discounts instead of four?
2. What would be the final price if the vendor had given a 20% discount followed by two 10% discounts?
3. How can the compound discount formula be generalized for any number of successive discounts?
4. What would the amount of fraud be if the original price was Rs 2000?
5. If the successive discounts were different (e.g., 15%, 10%, 5%, 10%), how would the final price be affected?

**Tip:** When dealing with successive discounts, remember that each discount is applied to the price after the previous discount has been deducted. This is why multiple small discounts often lead to a smaller reduction than a single equivalent large discount.

Learn how to calculate successive discounts and determine fraud amounts in a math problem involving percentages. Understand the application of percentage calculations and successive discounts with step-by-step solutions. Suitable for students in Grades 6-8.

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