Solving the Discount Problem: Finding Ram's Chair Price

This problem involves calculating the price Ram paid for a chair after receiving a discount. We are given the discount percentage and the amount saved due to the discount. We need to find the original market price and then determine the final price Ram paid.

Understanding the Given Information

• Discount Percentage: 35% on the market price.
• Amount saved due to discount: ₹245. This means the discount amount is ₹245.
• If there was no discount, Ram would pay ₹245 more, which is exactly the value of the 35% discount.

Calculating the Market Price (MP)

The discount amount (₹245) represents 35% of the Market Price (MP). We can set up an equation to find the MP.

Let MP be the Market Price of the chair.

\(35\% \text{ of } MP = ₹245\)

We can write this as:

\(\frac{35}{100} \times MP = 245\)

To find MP, we can rearrange the equation:

\(MP = \frac{245 \times 100}{35}\)

Now, let's perform the calculation:

\(MP = \frac{24500}{35}\)

We can simplify this by dividing both the numerator and the denominator by common factors. For example, both are divisible by 5:

\(MP = \frac{24500 \div 5}{35 \div 5} = \frac{4900}{7}\)

Now, divide 4900 by 7:

\(MP = 700\)

So, the Market Price of the chair was ₹700.

Calculating the Price Ram Paid

Ram bought the chair at a 35% discount on the market price. The price Ram paid is the Market Price minus the Discount Amount.

Price Paid = Market Price - Discount Amount

Price Paid = ₹700 - ₹245

Price Paid = ₹455

Alternatively, Ram paid \((100 - 35)\% = 65\%\) of the Market Price.

Price Paid = \(65\% \text{ of } ₹700\)

Price Paid = \(\frac{65}{100} \times 700\)

Price Paid = \(65 \times 7\)

Price Paid = ₹455

Both methods give the same result. Ram paid ₹455 for the chair.

Summary of the Calculation Steps

1. Identify the discount amount, which is the extra amount Ram would have paid without the discount (₹245).
2. Recognize that this discount amount is 35% of the market price.
3. Use the percentage information to set up an equation and solve for the market price.
4. Subtract the discount amount from the market price to find the price Ram paid.

Revision Table: Key Terms in Discount Problems

Additional Information: Discounts and Pricing

Discounts are common in retail and are used to attract customers or clear stock. Understanding how discounts work is important for both buyers and sellers.

• Discounts are almost always calculated on the original price, known as the Market Price or List Price.
• The Selling Price is what the customer finally pays after the discount is applied.
• Sometimes, successive discounts are offered. In such cases, the second discount is calculated on the price after the first discount, not on the original market price.
• Word problems involving discounts often require you to find one of the values (Market Price, Discount Amount, Selling Price, or Discount Percentage) when others are given. It's crucial to identify which value represents the base for the percentage calculation (usually the Market Price).