Two shopkeepers announce the same price of Rs.700 for a sewing machine.The first offers successive discounted 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 prices of both shopkeepers after applying their respective successive discounts on the marked price of Rs. 700.

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

1. **Calculate the first discount (30%):**
\[ \text{Price after first discount} = \text{Marked Price} \times (1 - \text{First Discount Percentage}) \]
\[ = 700 \times (1 - 0.30) = 700 \times 0.70 = 490 \]

2. **Calculate the second discount (6%):**
\[ \text{Selling Price} = \text{Price after first discount} \times (1 - \text{Second Discount Percentage}) \]
\[ = 490 \times (1 - 0.06) = 490 \times 0.94 = 460.60 \]

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

1. **Calculate the first discount (20%):**
\[ \text{Price after first discount} = \text{Marked Price} \times (1 - \text{First Discount Percentage}) \]
\[ = 700 \times (1 - 0.20) = 700 \times 0.80 = 560 \]

2. **Calculate the second discount (16%):**
\[ \text{Selling Price} = \text{Price after first discount} \times (1 - \text{Second Discount Percentage}) \]
\[ = 560 \times (1 - 0.16) = 560 \times 0.84 = 470.40 \]

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

\[ \text{Difference} = \text{Selling Price of Second Shopkeeper} - \text{Selling Price of First Shopkeeper} \]
\[ = 470.40 - 460.60 = 9.80 \]

### Final Answer
The difference in their selling price is Rs. 9.80.

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