Percentage tricks: fractions, swaps and successive change

प्रतिशत ट्रिक्स: भिन्न, अदला-बदली और क्रमागत परिवर्तन

Most percentage questions fall to four ideas: know the fraction for common percentages, swap x% of y, build any percentage from 10% and 1%, and use a + b + ab/100 for successive changes.

सामान्य प्रतिशत के भिन्न याद रखें, x% of y = y% of x, 10% और 1% से कोई भी प्रतिशत, और क्रमागत परिवर्तन के लिए a + b + ab/100।

Memorise these fraction values

Dividing by a small number is faster than multiplying by a percentage.

50% = 1/2, 25% = 1/4, 20% = 1/5, 10% = 1/10
12.5% = 1/8, 37.5% = 3/8, 62.5% = 5/8, 87.5% = 7/8
33⅓% = 1/3, 66⅔% = 2/3, 16⅔% = 1/6, 83⅓% = 5/6
14²⁄₇% = 1/7, 11¹⁄₉% = 1/9, 9¹⁄₁₁% = 1/11

Example 12.5% of 640

1/8 of 640 = 80

Example 37.5% of 96

3/8 × 96 = 3 × 12 = 36

Swap the numbers

x% of y is always equal to y% of x. Pick the easier way round.

Example 8% of 50

= 50% of 8 = 4

Example 16% of 25

= 25% of 16 = 4

Build any percentage from 10% and 1%

10% = move the decimal one place; 1% = two places. Add and subtract pieces.

Example 35% of 840

10% = 84 → 30% = 252, 5% = 42 → 294

Example 18% of 450

20% = 90, minus 2% = 9 → 81

Successive changes: a + b + ab/100

For two changes of a% and b% one after another (use minus for a decrease), the net change is a + b + (a × b)/100.

Example Price up 10%, then up 20%

10 + 20 + 200/100 = 32% increase

Example Discounts of 10% and 20%

−10 − 20 + 200/100 = −28%, a 28% total discount (not 30%)

Example Up 20%, then down 20%

20 − 20 − 400/100 = −4%: a 4% loss overall

Price rise and consumption

If a price rises by r%, consumption must fall by r ÷ (100 + r) × 100% to keep spending the same.

Example Petrol price up 25%

25 ÷ 125 = 1/5 → cut use by 20%

Try it yourself · अभ्यास

62.5% of 48 = ?
Show answer
5/8 × 48 = 30
Two successive increases of 10% equal a single increase of?
Show answer
10 + 10 + 1 = 21%
4% of 75 = ?
Show answer
75% of 4 = 3