A pair of shoes was sold for N2,250.00 at a loss of 10%. What was the cost price?

Analyze the question: The shoes were sold at a loss of 10%, so the selling price (SP) is 90% of the cost price (CP). We are given SP = N2,250 and need to find CP.

Concept:

• Loss means SP < CP.
• Loss % is always calculated on the cost price.
• SP = CP × (100 − Loss%)/100

Solution:

SP = (100 − 10)% of CP

2,250 = 0.90 × CP

CP = 2,250 ÷ 0.90

CP = N2,500

Check: 10% of 2,500 = 250, and 2,500 − 250 = 2,250 ✓

Why the other options are wrong:

• C (N2,538) comes from wrongly adding 10% of 2,250 to the SP (2,250 + 225 = 2,475 is close to this kind of error), which treats the loss as a percentage of the selling price instead of the cost price.
• A, D and E are distractors that do not satisfy the check.

Tip: For a loss, divide the SP by (1 − loss rate). For a gain, divide the SP by (1 + gain rate). Always take the percentage on the cost price, and do a quick check by working forward from your answer.