Finding the Marked Price of a Bike with Discount

This problem involves calculating the original price, also known as the marked price (MP), of a bike before a discount was applied. We are given the selling price (SP) and the percentage of discount offered.

Understanding Key Terms in Pricing

• Marked Price (MP): This is the price initially marked on the product. Discounts are usually calculated on the marked price.
• Selling Price (SP): This is the price at which the product is actually sold after deducting any discount from the marked price.
• Discount: This is the reduction in the marked price offered to the customer. It is usually expressed as a percentage of the marked price.
• Discount Percentage: The discount expressed as a percentage of the marked price.

Relationship Between Marked Price, Selling Price, and Discount

The fundamental relationship is:

Selling Price = Marked Price - Discount

The Discount can be calculated as:

Discount = Discount Percentage of Marked Price

So, substituting the second equation into the first, we get:

Selling Price = Marked Price - (Discount Percentage $\times$ Marked Price)

This can be simplified by taking Marked Price as a common factor:

Selling Price = Marked Price $\times$ (1 - Discount Percentage (in decimal form))

Applying the Formula to Find the Marked Price

We are given:

• Selling Price (SP) = ₹87,500
• Discount Percentage = 44%

First, convert the discount percentage to a decimal:

Discount Percentage (decimal) = $\frac{44}{100} = 0.44$

Now, use the formula:

SP = MP $\times$ (1 - Discount Percentage (decimal))

Substitute the given values:

₹87,500 = MP $\times$ (1 - 0.44)

₹87,500 = MP $\times$ (0.56)

To find the Marked Price (MP), rearrange the equation:

MP = $\frac{\text{₹}87,500}{0.56}

Calculating the Marked Price

Let's perform the division:

MP = $\frac{87500}{0.56}

To make the division easier, we can remove the decimal from the denominator by multiplying both the numerator and the denominator by 100:

MP = $\frac{87500 \times 100}{0.56 \times 100} = \frac{8750000}{56}

Now, divide 8750000 by 56:

\begin{align*} MP &= \frac{8750000}{56} \\ &= \frac{8750000 \div 8}{56 \div 8} \quad \text{(Dividing both by 8)} \\ &= \frac{1093750}{7} \quad \text{(Now divide 1093750 by 7)} \\ &= 156250 \end{align*}

So, the marked price of the bike is ₹1,56,250.

Verification

Let's verify if a 44% discount on ₹1,56,250 results in a selling price of ₹87,500.

Discount Amount = 44% of ₹1,56,250

Discount Amount = $0.44 \times 156250$

Discount Amount = ₹68,750

Selling Price = Marked Price - Discount Amount

Selling Price = ₹1,56,250 - ₹68,750

Selling Price = ₹87,500

This matches the given selling price, confirming our calculated marked price is correct.

The marked price of the bike is ₹1,56,250.

Revision Table: Price Calculation Concepts

Additional Information: Percentage Concepts

Understanding percentages is crucial for solving problems involving discounts, profit, and loss. A percentage represents a part out of a hundred.

• Converting Percentage to Decimal: Divide the percentage by 100. For example, 44% = 44/100 = 0.44.
• Calculating Percentage of a Value: Multiply the value by the percentage in decimal or fractional form. For example, 44% of 100 = 0.44 $\times$ 100 = 44.
• When a discount of 44% is given, it means the customer pays (100 - 44)% = 56% of the marked price. So, the selling price is 56% of the marked price.

This principle was used in the calculation: SP = 56% of MP, which is SP = 0.56 $\times$ MP.