Percentages • Topic 2 of 3

Discount and Simple Interest

What is Discount?

Discount is a reduction in the selling price of an item. It is usually expressed as a percentage of the Marked Price (MP) or List Price.

Important Terms:

  • Marked Price (MP): The original price printed on the item
  • Discount: The amount subtracted from MP
  • Selling Price (SP): The actual price paid after discount

Formulas:

ConceptFormula
Discount AmountMP × \(\frac{\text{Discount%}}{100}\)
Selling Price after DiscountMP - Discount = MP × \((1 - \frac{\text{Discount%}}{100})\)
Discount Percentage\(\frac{\text{Discount}}{MP} \times 100\%\)

What is Simple Interest?

Simple Interest (SI) is the extra money paid for borrowing money or earned on savings. It is calculated only on the original principal amount.

Key Terms:

  • Principal (P): The initial amount borrowed or invested
  • Rate (R): Interest rate per year (as percentage)
  • Time (T): Time period in years
  • Simple Interest (SI): Interest earned/paid
  • Amount (A): Principal + Interest

Simple Interest Formulas:

ConceptFormula
Simple Interest\(SI = \frac{P \times R \times T}{100}\)
Amount\(A = P + SI = P(1 + \frac{RT}{100})\)
Principal\(P = \frac{SI \times 100}{R \times T}\)
Rate\(R = \frac{SI \times 100}{P \times T}\)
Time\(T = \frac{SI \times 100}{P \times R}\)

Real-life Applications:

  • Bank loans and mortgages
  • Savings accounts interest
  • Festival sales discounts
  • "Buy one get one" offers
Discount and Simple InterestDISCOUNTMarked Price (MP)₹2,000Discount: 20% = ₹400Sale Price: ₹1,600Discount = MP × Rate/100SP = MP − DiscountSIMPLE INTERESTSI = P × R × T 100P = Principal (₹)R = Rate per annum (%)T = Time (years)A = Amount = P + SIe.g. SI = 5000×8×3/100 = ₹1200
1
Worked Example

A shop offers a 15% discount on a ₹1200 watch. Find the discount amount and the selling price.

Solution
  • Step 1: Discount = 15% of MP = \(\frac{15}{100} \times 1200\)
  • Step 2: Discount = \(0.15 \times 1200 = ₹180\)
  • Step 3: SP = MP - Discount = \(1200 - 180 = ₹1020\)

Answer: Discount = ₹180, Selling Price = ₹1020

2
Worked Example

Find the simple interest on ₹5000 for 3 years at 8% per annum. Also find the amount.

Solution
  • Step 1: P = ₹5000, R = 8%, T = 3 years
  • Step 2: \(SI = \frac{P \times R \times T}{100} = \frac{5000 \times 8 \times 3}{100}\)
  • Step 3: \(SI = \frac{120000}{100} = ₹1200\)
  • Step 4: Amount = P + SI = \(5000 + 1200 = ₹6200\)

Answer: Simple Interest = ₹1200, Amount = ₹6200

3
Worked Example

A television is marked at ₹25,000. It is sold at a discount of 12%. If the shopkeeper still makes a profit of 10%, find the cost price of the television.

Solution
  • Step 1: MP = ₹25,000, Discount = 12%
  • Step 2: SP = MP × \((1 - \frac{12}{100}) = 25000 \times 0.88 = ₹22,000\)
  • Step 3: Profit = 10%, so SP = CP × \((1 + \frac{10}{100}) = CP \times 1.1\)
  • Step 4: \(22000 = CP \times 1.1\)
  • Step 5: \(CP = \frac{22000}{1.1} = ₹20,000\)

Answer: Cost Price = ₹20,000

Key Points

  • Discount = MP × Discount% | SP after discount = MP - Discount
  • Simple Interest \(= \frac{P \times R \times T}{100}\)
  • Amount = Principal + Simple Interest
  • Discount and profit percentage are calculated on different bases (MP vs CP)
  • Simple interest is linear (same interest each year)
  • Time must be in years; convert months to years (divide by 12)
Tap an option to check your answer0 / 4
Q1.A discount is a reduction on the:
Explanation: Marked price.
Q2.Selling Price $=$
Explanation: MP minus discount.
Q3.Simple Interest $=$
Explanation: $\tfrac{PRT}{100}$.
Q4.Amount $=$
Explanation: $P+\text{SI}$.