Percentages & Discounts
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Lesson overview
Percentage change, reverse percentages, profit, loss, discount and VAT, simple and compound interest, and percentage error.
Go to lesson quiz →Exam guidance · JAMB UTME Speed Lens
Pacing
~40 seconds per MCQ (180 questions in 120 minutes, no negative marking).
How JAMB marks this
Fast dimensional/sign elimination and standard formula shortcuts — skip multi-line algebra when substitution tests options faster.
Watch out for
UTME distractors routinely include the intermediate value (e.g., forgetting to convert cm³ to dm³ or °C to Kelvin).
Lesson content
Overview
Percentages are everywhere in Nigerian life: a 15% discount at a Lagos supermarket, 7.5% VAT on a phone bill, 10% interest on a cooperative loan, a 25% rise in the price of a bag of rice. JAMB uses exactly these situations to test whether you can turn words into a short, correct calculation. This lesson covers percentage change, reverse percentages, profit and loss, discounts and VAT, simple and compound interest, and percentage error. One idea ties them together: a percentage change is a multiplication.
Key concept: percentages as multipliers
A percentage is a fraction with denominator 100: 15% = 15/100 = 0.15. To find p% of a quantity, multiply by p/100. To express A as a percentage of B, calculate (A ÷ B) × 100%. Percentage change = (change ÷ original value) × 100%. It is always measured against the original value. An increase of p% multiplies the original by (1 + p/100); a decrease of p% multiplies it by (1 − p/100). These numbers are called multipliers. Profit or loss percent is measured on the cost price. Discount is measured on the marked price. VAT (value added tax, 7.5% in Nigeria at the time of writing) is added to the selling price. Percentage error = (error ÷ true value) × 100%, where the error is the difference between the measured (or approximate) value and the true value.
Methods for each type of question
Percentage change. Find the actual change, divide by the original value, multiply by 100. A price rising from ₦200 to ₦250 has risen by 50/200 × 100% = 25%. Reverse percentages. If the value after a change is known, divide by the multiplier to get back to the original. Never take the percentage of the new value. Successive changes. Multiply the multipliers. Two increases of 10% give 1.1 × 1.1 = 1.21, an overall increase of 21%, not 20%, because the second 10% is taken on the already increased value. Profit and loss. Profit = selling price − cost price, and profit % = profit ÷ cost price × 100%. A loss is treated the same way. Discounts and VAT. Apply each multiplier in turn: discount first (on the marked price), then VAT on the discounted price, unless the question says otherwise. Simple interest. I = PRT/100, where P is the principal, R the rate per cent per year and T the time in years. The amount is A = P + I. Compound interest. Interest is added each year and itself earns interest, so A = P(1 + R/100)ⁿ after n years. The compound interest is A − P. Approximations and percentage error. Rounding to significant figures keeps the first non-zero digits: 34,567 is 34,600 to 3 significant figures, and 0.004576 is 0.0046 to 2 significant figures. Any rounding or measurement creates an error; express it as a percentage of the true value.
Formulae to know
Percentage change = (new − original) ÷ original × 100% Increase by p%: × (1 + p/100). Decrease by p%: × (1 − p/100) Original value = new value ÷ multiplier Profit % = (SP − CP) ÷ CP × 100% Simple interest: I = PRT/100. Compound amount: A = P(1 + R/100)ⁿ Percentage error = |measured − true| ÷ true × 100%
Worked example 1: discount, then VAT
A blender is marked ₦4,000. The shop gives a 15% discount, and then 7.5% VAT is added to the discounted price. How much does the customer pay?
Active Worked Example · Predict Step 1
3 stepsWrite down the formula, rule, or first move you would make before revealing Step 1.
Worked example 2: reverse percentage and profit
After a 20% increase, the price of a bag of garri is ₦6,000. What was the price before the increase? A trader bought the bag at the old price and sold it at the new price; find her percentage profit.
Active Worked Example · Predict Step 1
4 stepsWrite down the formula, rule, or first move you would make before revealing Step 1.
Worked example 3 (UTME standard): simple and compound interest
Mr Okafor invests ₦50,000 at 10% per annum for 3 years. Find the interest earned (a) at simple interest, (b) at compound interest, compounded yearly.
Active Worked Example · Predict Step 1
5 stepsWrite down the formula, rule, or first move you would make before revealing Step 1.
Common traps
• Dividing the change by the new value. Percentage change is always on the original. • Finding the original by subtracting the percentage of the new value. Divide by the multiplier. • Adding successive percentages: +20% then −20% is not 0%, it is −4%. • Measuring profit on the selling price. Profit and loss percentages use the cost price. • Using the simple-interest formula when interest is compounded.
Summary
• Percentage change = change ÷ original × 100%. • A change of p% multiplies by (1 ± p/100); reverse it by dividing by the multiplier. • Profit/loss % uses cost price; discount uses marked price; VAT is added afterwards. • Simple interest I = PRT/100; compound amount A = P(1 + R/100)ⁿ. • Percentage error = error ÷ true value × 100%.
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