Percentages • Topic 1 of 5

Percentage Basics & Conversions

Percent means "per hundred", so x% = x/100. The fastest CAT students never compute percentages the slow way — they memorise the fraction–percentage table (1/2=50%, 1/3≈33.33%, 1/4=25%, 1/5=20%, 1/6≈16.67%, 1/7≈14.28%, 1/8=12.5%, 1/9≈11.11%, 1/11≈9.09%, 1/12≈8.33%) and read questions in fractions. "37.5% of 64" is just (3/8)×64 = 24 in one step. To find what percentage one quantity is of another, divide and multiply by 100. Converting a decimal to a percent shifts the point two places right (0.45 → 45%); a percent to a decimal shifts it two places left.

✅ Solved examples

1. Find 62.5% of 240.
62.5% = 5/8. (5/8) × 240 = 5 × 30 = 150.
2. What percentage of 1.5 kg is 90 g?
1.5 kg = 1500 g. (90/1500) × 100 = 6%.
3. Convert 7/40 to a percentage.
(7/40) × 100 = 700/40 = 17.5%.
4. If 16⅔% of a number is 50, find the number.
16⅔% = 1/6. So (1/6) × N = 50 ⇒ N = 300.

✏️ Practice — try these, take hints as needed

1. Find 87.5% of 96.
87.5% = 7/8.
(7/8) × 96.
7 × 12.
84
2. What percent of 2 hours is 24 minutes?
Convert to the same unit.
2 h = 120 min.
(24/120) × 100.
20%
3. Express 0.375 as a percentage and as a fraction.
Decimal → percent: shift two places.
0.375 = 37.5%.
= 3/8.
37.5% = 3/8
4. 33⅓% of a number is 81. Find the number.
33⅓% = 1/3.
(1/3)N = 81.
N = 81 × 3.
243
5. A scored 45 out of 60. What percentage is that?
(45/60) × 100.
45/60 = 3/4.
3/4 = 75%.
75%

📝 Topic test — 8 questions

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