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🇨🇩 Problem solving

Commerce, percentages and interest

⏱ 20 minOfficial programme: CD-P5-PRO-01

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🎯 In this lesson, you will learn to

  • Solve discount, markdown, price rise and exchange-rate problems.
  • Use the simple rule of three, percentages, scale, intervals and simple interest.

The lesson

Introduction

At the Zando market in Kinshasa, traders give discounts, and prices sometimes go up. Some families put their savings in a savings cooperative that pays them interest. In this lesson, you solve trade problems: discounts, markdowns, cash discounts, price rises and exchange rates, as well as problems on the rule of three, scale, intervals and interest.

Explanation

Price reductions

  • a markdown: for damaged or out-of-fashion goods;
  • a discount: for a loyal customer or a large purchase;
  • a cash discount: for paying in cash or in advance.

Net price = starting price − reduction. A price rise is added: new price = old price + rise.

Percentage: a 10% reduction on 30 000 FC is worth 30 000 × 10 ÷ 100 = 3 000 FC.

Explanation

Simple rule of three: go through one unit. If 5 exercise books cost 7 500 FC, 1 book costs 7 500 ÷ 5 = 1 500 FC, and 8 books cost 8 × 1 500 = 12 000 FC.

Scale: on a map at the scale 1 : 100 000, 1 cm stands for 100 000 cm, that is 1 km.

Intervals: on a line, if objects are placed at both ends, there is one more object than intervals. For 20 m with a post every 5 m: 20 ÷ 5 = 4 intervals, so 5 posts.

Explanation

Exchange rate. To pay in a foreign currency, we use an exchange rate. If 1 unit of that currency is worth 2 800 FC, then 5 units are worth 5 × 2 800 = 14 000 FC, and 28 000 FC are worth 28 000 ÷ 2 800 = 10 units.

Simple interest. A capital CC invested at a yearly rate tt (in %) for nn years earns interest:
I=C×t×n100I = \frac{C \times t \times n}{100}
If the time is given in months, divide again by 12.

Worked example

A school uniform costs 30 000 FC. The tailor gives a 10% discount to a family that buys several. What is the net price of one uniform?

Step 1: Discount: 30 000 × 10 ÷ 100 = 3 000 FC.

Step 2: Net price: 30 000 − 3 000 = 27 000 FC.

Answer: the uniform costs 27 000 FC.

Worked example

On a map at the scale 1 : 100 000, two villages are 7 cm apart. What is the real distance?

Step 1: 1 cm on the map stands for 100 000 cm in reality.

Step 2: 7 × 100 000 = 700 000 cm.

Step 3: 700 000 cm = 7 000 m = 7 km.

Answer: the villages are 7 km apart.

Worked example

Ngalula puts 200 000 FC in a savings cooperative, at a rate of 6% per year, for 2 years. Calculate the interest, then the amount she will have at the end.

Step 1: I=200 000×6×2100I = \frac{200\,000 \times 6 \times 2}{100}.

Step 2: 200 000 × 6 × 2 = 2 400 000; 2 400 000 ÷ 100 = 24 000 FC.

Step 3: Capital + interest: 200 000 + 24 000 = 224 000 FC.

Answer: the interest is 24 000 FC; Ngalula will have 224 000 FC.

Watch out

Watch out: a 10% rise followed by a 10% fall does not bring you back to the starting price. For 10 000 FC: the rise gives 11 000 FC, then the 10% fall on 11 000 FC (1 100 FC) gives 9 900 FC. Each percentage is calculated on the current price.

Key points

  • Markdown, discount, cash discount: take the reduction away from the price; a rise is added.
  • x% of a price = price × x ÷ 100.
  • Rule of three: go through one unit.
  • Scale 1 : 100 000: 1 cm on the map = 1 km in reality.
  • Intervals with objects at both ends: objects = intervals + 1.
  • Simple interest: I=C×t×n100I = \frac{C \times t \times n}{100}.

✍️ Exercises

Answer one exercise at a time. Your answer is checked right away, with an explanation.

Exercise 1 of 9

★ Easy

Calculate 20% of 15 000 FC.

FC

You can use a decimal comma or point (2,5 or 2.5).