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Discount Problems - Civil Service Exam

Introduction to Discount Problems

Discount problems are common in real-life shopping scenarios and appear frequently in math sections of exams, including the civil service exam. Understanding how to calculate discounts helps in finding the best deals, managing finances, and solving related math questions effectively.

Key Concepts in Discount Problems

  1. Original Price (Marked Price): The initial price of an item before any discount is applied.
  2. Discount Rate: The percentage reduction applied to the original price.
  3. Discount Amount: The actual amount subtracted from the original price, calculated using the discount rate.
  4. Sale Price (Discounted Price): The final price paid after applying the discount.

Key Formulas

  1. Discount Amount:

    Discount=Original Price × Discount  Rate /100

  2. Sale Price:

Step-by-Step Approach to Solving Discount Problems

  1. Identify the Variables: Note the original price, discount rate, and what you need to find (discount amount or sale price).
  2. Calculate the Discount Amount: Use the discount formula to find the amount reduced from the original price.
  3. Determine the Sale Price: Subtract the discount amount from the original price to get the final cost.

Example Problem

Problem:
A shirt costs PHP 800 and is on sale with a 15% discount. What is the sale price of the shirt?

Solution:

  1. Identify the variables:

    • Original Price = PHP 800
    • Discount Rate = 15%

  2. Calculate the Discount Amount:

    Discount=800 × 15/100 = 800 × 0.15 = 120
  3. Determine the Sale Price:
  4. Sale Price = 800 − 120 = 680

Answer: The sale price of the shirt is PHP 680.

Variations in Discount Problems

  1. Finding the Original Price Given the Sale Price and Discount Rate:

    • Use the formula: Original Price = Sale Price / 1 − Discount Rate / 100

  2. Finding the Discount Rate Given the Original and Sale Price:

    • Use the formula: Discount Rate = Original Price − Sale Price / Original Price × 100

Key Tips for the Exam

  • Always double-check calculations, especially percentage conversions.
  • Understand which variable you are solving for to avoid confusion.
  • Use estimation to quickly assess if your answer makes sense.

Discount Problems Exercises

1.  A department store in Manila has a sale on a blender that was originally priced at PHP 2,400. The sale price is PHP 1,920. What was the discount rate?

2. A local shoe store reduced the price of a pair of sneakers from PHP 3,000 to PHP 2,250. What was the discount rate?

3. A bookstore in Cebu marked down a cookbook from PHP 850 to PHP 680 during a special sale. What was the discount rate?

4. Carlo bought a pair of jeans for PHP 1,200 after a 20% discount. What was the original price of the jeans?

5. Liza purchased a microwave oven for PHP 3,400 after a 15% discount. What was the original price of the microwave?

6. Jenny bought an air conditioner for PHP 16,000 after a 20% discount. What was the original price of the air conditioner?

7. Marie bought a dining table originally priced at ₱8,000. After a discount, she paid only ₱6,000. What was the percentage of the discount?

8.  Carlos purchased a laptop for ₱50,000, but with a store promotion, he only paid ₱37,500. What was the percentage of the discount?

9. Ana bought a pair of curtains priced originally at ₱3,000. After receiving a discount, she paid only ₱2,250. What was the percentage of the discount?

 
 
 
 

Answer Keys

Problem One:

A department store in Manila has a sale on a blender that was originally priced at PHP 2,400. The sale price is PHP 1,920. What was the discount rate?

Choices:

A) 15% discount

B) 20% discount

C) 25% discount

D) 30% discount

Answer: B) 20% discount

Solution:

  1. Discount Calculation: Original Price – Sale Price = PHP 2,400 – PHP 1,920 = PHP 480.
  2. Discount Rate Calculation: (Discount / Original Price) * 100% = (PHP 480 / PHP 2,400) * 100% = 20%.

The discount rate on the blender is 20%.

Problem Two:

A local shoe store reduced the price of a pair of sneakers from PHP 3,000 to PHP 2,250. What was the discount rate?

Choices:

A) 20% discount

B) 25% discount

C) 30% discount

D) 35% discount

Answer: B) 25% discount

Solution:

  1. Discount Calculation: Original Price – Sale Price = PHP 3,000 – PHP 2,250 = PHP 750.
  2. Discount Rate Calculation: (Discount / Original Price) * 100% = (PHP 750 / PHP 3,000) * 100% = 25%.

The discount rate on the pair of sneakers is 25%.

Problem Three:

A bookstore in Cebu marked down a cookbook from PHP 850 to PHP 680 during a special sale. What was the discount rate?

Choices:

A) 15% discount

B) 18% discount

C) 20% discount

D) 25% discount

Answer: C) 20% discount

Solution:

  1. Discount Calculation: Original Price – Sale Price = PHP 850 – PHP 680 = PHP 170.
  2. Discount Rate Calculation: (Discount / Original Price) * 100% = (PHP 170 / PHP 850) * 100% = 20%.

The discount rate on the cookbook is 20%.

Problem Four:

Carlo bought a pair of jeans for PHP 1,200 after a 20% discount. What was the original price of the jeans?

Choices:

A) PHP 1,440

B) PHP 1,500

C) PHP 1,350

D) PHP 1,425

Answer: B) PHP 1,500

Solution:

  1. Discount Rate: 20%
  2. Sale Price: PHP 1,200
  3. Calculation for Original Price: Let X be the original price. After a 20% discount, Carlo paid PHP 1,200, so:
    X
  4. Solving for X:

The original price of the jeans was PHP 1,500.

Problem Five:

Liza purchased a microwave oven for PHP 3,400 after a 15% discount. What was the original price of the microwave?

Choices:

A) PHP 3,750

B) PHP 3,900

C) PHP 4,000

D) PHP 4,100

Answer: C) PHP 4,000

Solution:

  1. Discount Rate: 15%
  2. Sale Price: PHP 3,400
  3. Calculation for Original Price: Let X be the original price. After a 15% discount, Liza paid PHP 3,400, so:
  4. Solving for X:

The original price of the microwave was PHP 4,000.

Problem Six:

Jenny bought an air conditioner for PHP 16,000 after a 20% discount. What was the original price of the air conditioner?

Choices:

A) PHP 19,200

B) PHP 19,500

C) PHP 20,000

D) PHP 20,500

Answer: C) PHP 20,000

Solution:

  1. Discount Rate: 20%
  2. Sale Price: PHP 16,000
  3. Calculation for Original Price: Let X be the original price. After a 20% discount, Jenny paid PHP 16,000, so:
    X
  4. Solving for X:

The original price of the air conditioner was PHP 20,000.

Problem Seven:

Marie bought a dining table originally priced at ₱8,000. After a discount, she paid only ₱6,000. What was the percentage of the discount?

Choices:

A) 20%

B) 25%

C) 30%

D) 35%

Correct Answer: B) 25%

Solution: The original price was ₱8,000 and the sale price was ₱6,000. The discount amount is ₱8,000 – ₱6,000 = ₱2,000.

The percentage of the discount is:

Problem Eight:

Carlos purchased a laptop for ₱50,000, but with a store promotion, he only paid ₱37,500. What was the percentage of the discount?

Choices:

A) 20%

B) 25%

C) 30%

D) 35%

Correct Answer: B) 25%

Solution: The original price was ₱50,000 and the sale price was ₱37,500. The discount amount is ₱50,000 – ₱37,500 = ₱12,500.

The percentage of the discount is:

(12,500/50,000)×100% = 25%

Problem Nine:

Ana bought a pair of curtains priced originally at ₱3,000. After receiving a discount, she paid only ₱2,250. What was the percentage of the discount?

Choices:

A) 20%

B) 25%

C) 30%

D) 35%

Correct Answer: B) 25%

Solution: The original price was ₱3,000 and the sale price was ₱2,250. The discount amount is ₱3,000 – ₱2,250 = ₱750.

The percentage of the discount is:

(750/3,000)×100% = 25%
 
 

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