A trader made a loss of 15% when an article was sold. Find the ratio of the selling price  : cost price

Analyze the question

A loss of 15% means the article was sold for 15% less than what it cost. We need the ratio SP : CP.

Concept

Loss = CP − SP, and Loss % = (Loss / CP) × 100. So when there is a loss of 15%:

SP = CP − 15% of CP = (100% − 15%) of CP = 85% of CP

Solution

Let CP = ₦100 (any value works).

• Loss = 15% of 100 = ₦15
• SP = 100 − 15 = ₦85

Ratio SP : CP = 85 : 100

Divide both sides by 5:

85 ÷ 5 = 17 and 100 ÷ 5 = 20

So SP : CP = 17 : 20

Answer

Why the other options are wrong

• A (3:20) uses the loss (15) against CP (100), so it is Loss : CP, not SP : CP.
• B (3:17) is Loss : SP.
• D (20:23) does not come from any correct step here.

Exam tip

For loss, SP = (100 − loss%) of CP. For profit, SP = (100 + profit%) of CP. So SP : CP is always (100 ± %) : 100. Then simplify the ratio. Here that is 85 : 100 = 17 : 20.