Kunal sold two bicycles—A and B. Marked Price of bicycle A was ₹500 more than that of bicycle B. He sold bicycle A at ₹ l620 after giving successive discounts of `20%` and `10%` on its marked price. What was the selling price of bicycle B, if Kunal sold it at a discount of `20%` on its marked price? (in₹)

Options

A. 1800
B. 1750
C. 1400
D. 1250

Answer

To solve the problem step-by-step, let's break it down:

### Step 1: Define the Marked Prices
Let the marked price of bicycle B be \( x \).
Then, the marked price of bicycle A will be \( x + 500 \).

### Step 2: Calculate Selling Price of Bicycle A
Kunal sold bicycle A for ₹1620 after giving successive discounts of 20% and 10%.

### Step 3: Calculate the Effective Selling Price Formula
The selling price after successive discounts can be calculated using the formula:
\[ \text{Selling Price} = \text{Marked Price} \times (1 - \text{Discount1}) \times (1 - \text{Discount2}) \]
For bicycle A:
\[ 1620 = (x + 500) \times (1 - 0.20) \times (1 - 0.10) \]
This simplifies to:
\[ 1620 = (x + 500) \times 0.80 \times 0.90 \]
\[ 1620 = (x + 500) \times 0.72 \]

### Step 4: Solve for Marked Price of Bicycle A
Now, rearranging the equation:
\[ x + 500 = \frac{1620}{0.72} \]
Calculating the right side:
\[ x + 500 = 2250 \]
Now, subtracting 500 from both sides:
\[ x = 2250 - 500 \]
\[ x = 1750 \]

### Step 5: Calculate Selling Price of Bicycle B
Now that we have the marked price of bicycle B as ₹1750, we need to find the selling price when Kunal sold it at a discount of 20%.
Using the formula for selling price:
\[ \text{Selling Price of B} = \text{Marked Price of B} \times (1 - \text{Discount}) \]
\[ \text{Selling Price of B} = 1750 \times (1 - 0.20) \]
\[ \text{Selling Price of B} = 1750 \times 0.80 \]
Calculating this gives:
\[ \text{Selling Price of B} = 1400 \]

### Final Answer
The selling price of bicycle B is ₹1400.

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