Technique 15 of 21

Percentage–fraction equivalents

प्रतिशत–भिन्न समतुल्य

The 1/2 to 1/20 table, the "x% of y = y% of x" swap and successive percentages in one line.

When to use it · कब उपयोग करें

Almost every percentage, profit-loss, discount and data-interpretation question.

लगभग हर प्रतिशत, लाभ-हानि, छूट और डेटा इंटरप्रिटेशन प्रश्न।

The method · विधि

1. Convert awkward percentages to fractions · असुविधाजनक प्रतिशत को भिन्न में बदलें

   12.5% = 1/8, 16.67% = 1/6, 14.28% = 1/7, 37.5% = 3/8, 8.33% = 1/12, 6.25% = 1/16. 37.5% of 480 = 3/8 × 480 = 180. 14.28% of 350 = 1/7 × 350 = 50. 8.33% of 2400 = 1/12 × 2400 = 200.

   12.5% = 1/8, 16.67% = 1/6, 14.28% = 1/7, 37.5% = 3/8, 8.33% = 1/12, 6.25% = 1/16। 480 का 37.5% = 3/8 × 480 = 180। 350 का 14.28% = 1/7 × 350 = 50। 2400 का 8.33% = 1/12 × 2400 = 200।

2. Swap the two numbers · दोनों संख्याएँ बदल दें

   x% of y = y% of x. 18% of 50 is the same as 50% of 18 = 9. Pick the version that is easier.

   y का x% = x का y%। 50 का 18% वही है जो 18 का 50% = 9। जो रूप आसान हो वही चुनें।

3. Successive percentage change · क्रमिक प्रतिशत परिवर्तन

   Two changes a% and b% combine to a + b + ab/100 %. +20% then +25%: 20 + 25 + 5 = 50%. +20% then −20%: 20 − 20 − 4 = −4%.

   दो परिवर्तन a% और b% मिलकर a + b + ab/100 % होते हैं। +20% फिर +25%: 20 + 25 + 5 = 50%। +20% फिर −20%: 20 − 20 − 4 = −4%।

Worked examples · हल किए उदाहरण

Why it works · यह क्यों काम करता है

x% of y = xy/100 = y% of x. Successive changes multiply: (1 + a/100)(1 + b/100) − 1 expands to a + b + ab/100 in percent.

y का x% = xy/100 = x का y%। क्रमिक परिवर्तन गुणित होते हैं: (1 + a/100)(1 + b/100) − 1 प्रतिशत में a + b + ab/100 बनता है।

Practise this technique Practice questions are part of the Pro Pass; a few samples are free.

Related techniques

Open the cheat sheets for squares, cubes, fractions and divisibility rules.