Two shopkeepers announce the same price of Rs 700 for a sewing machine. The first offers successive discounts of 30% and 6% while the second offers successive discounts of 20% and 16%. The difference in their selling price is

Options

A. Rs 9.8
B. Rs 16.8
C. Rs 22.4
D. Rs 36.4

Answer

To solve the problem, we need to calculate the selling price of the sewing machine for both shopkeepers after applying their respective discounts. Then, we will find the difference between the two selling prices.

### Step 1: Calculate the Selling Price for the First Shopkeeper
The first shopkeeper offers successive discounts of 30% and 6%.

1. **Calculate the first discount (30%)**:
\[ \text{First Discount} = 30\% \text{ of } 700 = \frac{30}{100} \times 700 = 210 \]
\[ \text{Price after first discount} = 700 - 210 = 490 \]

2. **Calculate the second discount (6%)**:
\[ \text{Second Discount} = 6\% \text{ of } 490 = \frac{6}{100} \times 490 = 29.4 \]
\[ \text{Selling Price for First Shopkeeper} = 490 - 29.4 = 460.6 \]

### Step 2: Calculate the Selling Price for the Second Shopkeeper
The second shopkeeper offers successive discounts of 20% and 16%.

1. **Calculate the first discount (20%)**:
\[ \text{First Discount} = 20\% \text{ of } 700 = \frac{20}{100} \times 700 = 140 \]
\[ \text{Price after first discount} = 700 - 140 = 560 \]

2. **Calculate the second discount (16%)**:
\[ \text{Second Discount} = 16\% \text{ of } 560 = \frac{16}{100} \times 560 = 89.6 \]
\[ \text{Selling Price for Second Shopkeeper} = 560 - 89.6 = 470.4 \]

### Step 3: Calculate the Difference in Selling Prices
Now, we can find the difference between the selling prices of the two shopkeepers.

\[ \text{Difference} = \text{Selling Price of Second Shopkeeper} - \text{Selling Price of First Shopkeeper} \]
\[ \text{Difference} = 470.4 - 460.6 = 9.8 \]

### Final Answer
The difference in their selling price is **Rs 9.8**.

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