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Ratios, Profit and Loss

10 min read

Ratio

A ratio compares quantities of the same kind. If a class has 12 girls and 8 boys, the ratio of girls to boys is . Divide both numbers by their common factor 4 to simplify: .

Sharing in a ratio

3 + 2 = 5 equal parts. Each part is 10 000. Amina gets 3 parts, Juma gets 2 parts.
Sharing in a ratioA bar split into five equal parts to share 3000 shillings in the ratio 3 to 2. Three parts, 1800 shillings, go to the first person and two parts, 1200 shillings, go to the second.6006006006006003 parts = 18002 parts = 1200Share 3000 in the ratio 3 : 2 → 5 parts, 3000 ÷ 5 = 600 each
Another example drawn as a bar: five equal parts, three for one person and two for the other.
Worked exampleShare an amount

Share 50 000 shillings between Amina and Juma in the ratio .

  1. Add the parts.
  2. Find one part.
  3. Multiply by each share.

Answer: Amina gets 30 000 and Juma gets 20 000 shillings.

Profit and loss

A trader buys goods at a cost price and sells them at a selling price. If the selling price is higher there is a profit. If it is lower there is a loss.

For a loss, swap the two prices and call the answer loss.
Try itBuy and sell

Set the cost price and the selling price. Positive numbers are profit, negative numbers are loss.

Worked exampleProfit percentage

A shopkeeper buys a radio for 40 000 shillings and sells it for 46 000 shillings. Find the profit percentage.

  1. Profit.
  2. As a percentage of the cost price.

Answer: The profit is 15%.

Check yourself Simplify the ratio 18 : 24.
Check yourself An item costing 5 000 is sold for 4 000. What is the loss percentage?

Key terms

Ratio
A comparison of two or more quantities of the same kind.
Cost price
What the seller paid for the goods.
Selling price
What the goods are sold for.
Profit / loss
The difference between selling price and cost price.

Summary

  • Simplify a ratio by dividing every part by the same number.
  • To share in a ratio: add the parts, find one part, multiply.
  • Profit = selling price − cost price; loss = cost price − selling price.
  • Profit or loss percentage is always taken from the cost price.
Numbers (II) Coordinate Geometry