# How to Solve Discount Problems

The Civil Service Examinations offer various types of math problems which may change from one examination to another. Two types of math problems that will likely appear are discount and interest problems. In this post, we will tackle discount problems.

The tag price that you see on items are their marked price. The sale price is the price that you pay after the discount has been made. If an item costs Php100 (marked price) and has a 10% discount, then you have to subtract the 10% of 100 from 100. Therefore, that item will cost Php100 – Php10 = Php90. Php90 is the sale price.

Note that in solving discount problems, you must know how to convert percent to decimals.  You need to convert percent to decimals (just divide by 100) in order to perform the calculation.

Sample Problem 1

A movie DVD which costs 600 is marked “25% off.” What is the discount? What is its sale price?

Solution

Discount = 25% of Php600 or (Php600 × 0.25) = Php150.00

Sale price = Php600 – Php150 = Php450.00

So, the discount is Php150 and the sale price is Php450.

Note that 0.25 is the decimal equivalent of 25%.

Sample Problem 2

Anna shops in an international store. A t-shirt with a tag price \$42 is marked “save 20%.” How much will Anna have to pay for the t-shirt if she were to buy it?

Solution

Discount = 20% of \$42 or (\$42 × 0.20) = \$8.40

Sale Price = \$42.00 – \$8.40 = \$33.60

Therefore, Anna will have to pay \$33.60 if she wants to buy the t-shirt.

Although it seldom happens in the real world, a discounted price might also be given in a Civil Service Exam problem. In this type of problem, the task is to find the original price (marked price) like the problem below.

Sample Problem 3

After getting a 10% discount, Nina bought a sofa for only 7200. What was the original price of the sofa?

Solution

We can use this equation to solve the problem above.

Marked Price – Discount Price = Sale Price

Now, if we let $x$ be the marked price of the sofa, then the discount price is 10% multiplied by $x$ or $0.1x$.

So, substituting to the equation above, we have

$x - 0.1x = 7200$

$0.9x = 7200$

To eliminate the decimal point, multiply both sides by $10$.

$9x = 72000$

Dividing both sides by 9, we have $8000$.

Therefore, the marked price of the sofa is Php8000. In the next post, we will discuss about strategies and short-cuts in solving discount problems.

Now that you have understood that concept of discount, you may want to read about the strategies and shortcuts on how to solve discount problems or take a quiz on discount problems.

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1. June 7, 2014

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2. June 9, 2014

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3. June 10, 2014

[…] 1. How to Solve Discount Problems discusses the basic concepts of discount problems, the common terminologies used, and some worked examples on how to solve such problems. […]