A salesperson, with a view to promote sales of an item, applies the priciple of simple interest. He declares that 300 pieces of the item can be obtained immediately against cash payment, but a customer will get only 200 pieces of the item if he defers the payment for a year. What is the rate percentage of interest on the whole?

Options

A. 30
B. 25
C. 50
D. 40

Answer

To solve the problem, we need to determine the rate of interest based on the information provided about the sales items and their pricing.

### Step-by-Step Solution:

1. **Identify the Cash Payment for Immediate Purchase:**
- The salesperson offers 300 pieces of an item for immediate cash payment. Let's assume the cash payment for 300 pieces is \( P \).

2. **Identify the Deferred Payment Offer:**
- If the customer defers the payment for a year, they only receive 200 pieces of the item.

3. **Calculate the Value of the Items:**
- Let’s assume the cash payment for 300 pieces is \( P = 600 \) rupees. Therefore, the price per piece is:
\[ \text{Price per piece} = \frac{600}{300} = 2 \text{ rupees} \]
- The value of 200 pieces would then be:
\[ \text{Value of 200 pieces} = 200 \times 2 = 400 \text{ rupees} \]

4. **Calculate the Savings:**
- If the customer defers the payment, they save the cost of 100 pieces (since they would have paid for 300 pieces but only receive 200). The cost for these 100 pieces is:
\[ \text{Cost of 100 pieces} = 100 \times 2 = 200 \text{ rupees} \]

5. **Determine the Interest Earned:**
- The customer effectively saves 200 rupees by deferring payment for one year. This 200 rupees represents the interest on the amount they would have paid for the additional 100 pieces.

6. **Calculate the Rate of Interest:**
- The formula for simple interest is given by:
\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \]
- Here, the principal is the amount that would have been paid for the 100 pieces (200 rupees), the interest earned is 200 rupees, and the time is 1 year. Rearranging the formula to find the rate:
\[ \text{Rate} = \frac{\text{Interest}}{\text{Principal} \times \text{Time}} = \frac{200}{200 \times 1} = 1 \]
- To express this as a percentage, we multiply by 100:
\[ \text{Rate} = 1 \times 100 = 100\% \]

7. **Final Calculation:**
- However, since the customer receives 200 pieces instead of 300, we need to consider the effective rate of interest on the total value of the items:
\[ \text{Effective Rate} = \frac{200}{400} \times 100 = 50\% \]

### Conclusion:
The rate percentage of interest on the whole is **50%**.