A shopkeepers announce the same price of Rs. 700 for a shirt. The first offers successive discounts of 30% and 6% while the second offers successive discounts of 20% and 16%. The shopkeeper that offers better discount is more of

Options

A. Rs. 22.40
B. Rs. 16.80
C. Rs. 9.80
D. Rs. 36.40

Answer

To determine which shopkeeper offers a better discount, we will calculate the total discount for both shopkeepers step by step.

### Step 1: Calculate the total discount for the first shopkeeper.
1. **Initial Price of the Shirt**: Rs. 700
2. **First Discount**: 30%
- Calculate the amount of the first discount:
\[ \text{First Discount} = 30\% \text{ of } 700 = \frac{30}{100} \times 700 = 210 \]
- Subtract this discount from the initial price:
\[ \text{Price after First Discount} = 700 - 210 = 490 \]

3. **Second Discount**: 6%
- Calculate the amount of the second discount on the new price:
\[ \text{Second Discount} = 6\% \text{ of } 490 = \frac{6}{100} \times 490 = 29.4 \]
- Subtract this discount from the price after the first discount:
\[ \text{Final Price after Second Discount} = 490 - 29.4 = 460.6 \]

4. **Total Discount for the First Shopkeeper**:
- Total discount is the sum of both discounts:
\[ \text{Total Discount} = 210 + 29.4 = 239.4 \]

### Step 2: Calculate the total discount for the second shopkeeper.
1. **Initial Price of the Shirt**: Rs. 700
2. **First Discount**: 20%
- Calculate the amount of the first discount:
\[ \text{First Discount} = 20\% \text{ of } 700 = \frac{20}{100} \times 700 = 140 \]
- Subtract this discount from the initial price:
\[ \text{Price after First Discount} = 700 - 140 = 560 \]

3. **Second Discount**: 16%
- Calculate the amount of the second discount on the new price:
\[ \text{Second Discount} = 16\% \text{ of } 560 = \frac{16}{100} \times 560 = 89.6 \]
- Subtract this discount from the price after the first discount:
\[ \text{Final Price after Second Discount} = 560 - 89.6 = 470.4 \]

4. **Total Discount for the Second Shopkeeper**:
- Total discount is the sum of both discounts:
\[ \text{Total Discount} = 140 + 89.6 = 229.6 \]

### Step 3: Compare the total discounts.
- **Total Discount for First Shopkeeper**: Rs. 239.4
- **Total Discount for Second Shopkeeper**: Rs. 229.6

### Conclusion:
The first shopkeeper offers a better discount. The difference in discounts is:
\[ 239.4 - 229.6 = 9.8 \]
Thus, the first shopkeeper offers a better discount of Rs. 9.8 more than the second shopkeeper.

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