Percentage

About 6 min · Mathematics · English

Time worked out from the lesson's 369 words at 150 words a minute, plus a minute for each question.

Percentage is one of the most fundamental topics in MPESB mathematics. It forms the backbone for several advanced topics including Profit and Loss, Simple and Compound Interest, Data Interpretation, and even questions on population growth or depreciation. Mastering percentage calculations is non-negotiable for scoring well.

Key ideas

Basic definition: x% means x/100. So 25% = 25/100 = 1/4 = 0.25.
Converting fraction to percentage: Multiply the fraction by 100. For example, 3/5 = (3/5) × 100 = 60%.
Converting percentage to fraction: Divide by 100 and simplify. For example, 37.5% = 37.5/100 = 3/8.
Percentage of a quantity: x% of A = (x/100) × A. Always identify what "of" refers to — that's your base.
Percentage increase/decrease: Change% = (Change / Original) × 100. The denominator is always the original value, not the new value.

Watch out for

Wrong base selection: Students often calculate percentage change using the new value as base instead of the original value. Remember — for percentage change, always divide by the ORIGINAL quantity.
Sign errors in successive changes: When applying the formula a + b + (ab/100), students forget that a decrease is negative. If price decreases by 20%, use a = −20, not +20.
Confusing "by" and "to": "Increased by 20%" means new value = 120% of original. "Increased to 120" means the new value IS 120. Read carefully.

Quick reference

x% of A = (x × A) / 100 — always multiply then divide by 100.
% Change = (Difference / Original) × 100 — denominator is always ORIGINAL.
Successive changes a% and b% → Net = a + b + (ab/100)% — use signs correctly.
To find original after x% increase → Multiply new value by 100/(100+x).
Memorize: 1/8 = 12.5%, 1/6 = 16.67%, 1/3 = 33.33%, 2/3 = 66.67%.

Check yourself: 3 questions

1. In a class of 80 students, 60% are boys. How many girls are there in the class?
2. A shopkeeper marks his goods 25% above the cost price and then gives a discount of 10%. What is his net profit percentage?
3. If the price of rice increases by 20%, by what percentage should a family reduce its consumption so that the expenditure on rice remains the same?

This lesson is cut from the topic's note, not rewritten. Fact-checked on 17 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.

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