{"id":4179,"date":"2025-06-06T14:22:10","date_gmt":"2025-06-06T14:22:10","guid":{"rendered":"https:\/\/diznr.com\/?p=4179"},"modified":"2025-06-06T14:22:10","modified_gmt":"2025-06-06T14:22:10","slug":"mathematics-short-tricks-percentage-math","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/mathematics-short-tricks-percentage-math\/","title":{"rendered":"Mathematics Short Tricks\/ MATH PERCENTAGE"},"content":{"rendered":"

Mathematics Short Tricks\/ MATH PERCENTAGE<\/p>\n

[fvplayer id=”644″]<\/p>\n

\u00a0Mathematics Short Tricks \u2013 Percentage\u00a0<\/strong><\/h3>\n

Percentages are one of the most important topics in competitive exams like SSC, Banking, GATE, CAT, etc.<\/strong> Here are some quick tricks & formulas<\/strong> to solve percentage problems FAST!<\/p>\n

\u00a0Basic Percentage Formula<\/strong><\/h3>\n

Percentage=(ValueTotal\u00a0Value)\u00d7100\\text{Percentage} = \\left(\\frac{\\text{Value}}{\\text{Total Value}}\\right) \\times 100<\/span>Percentage<\/span><\/span>=<\/span><\/span>(<\/span><\/span>Total\u00a0Value<\/span>Value<\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>\u00d7<\/span><\/span>100<\/span><\/span><\/span><\/span><\/span><\/p>\n

Example:<\/strong> If a student scores 45 marks<\/strong> out of 60<\/strong>, what is the percentage?<\/p>\n

(4560)\u00d7100=75%\\left(\\frac{45}{60}\\right) \\times 100 = 75\\%<\/span>(<\/span><\/span>6045<\/span>\u200b<\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>\u00d7<\/span><\/span>100<\/span>=<\/span><\/span>75%<\/span><\/span><\/span><\/span><\/span><\/p>\n

\u00a0Fast Conversion Between Fractions & Percentages<\/strong><\/h3>\n

Memorizing common fraction-percentage<\/strong> conversions will save time!<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Fraction<\/th>\nPercentage<\/th>\n<\/tr>\n<\/thead>\n
1\/2<\/td>\n50%<\/td>\n<\/tr>\n
1\/3<\/td>\n33.33%<\/td>\n<\/tr>\n
1\/4<\/td>\n25%<\/td>\n<\/tr>\n
1\/5<\/td>\n20%<\/td>\n<\/tr>\n
1\/6<\/td>\n16.66%<\/td>\n<\/tr>\n
1\/7<\/td>\n14.28%<\/td>\n<\/tr>\n
1\/8<\/td>\n12.5%<\/td>\n<\/tr>\n
1\/9<\/td>\n11.11%<\/td>\n<\/tr>\n
1\/10<\/td>\n10%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Example Trick:<\/strong> If you see 1\/5<\/strong>, immediately think 20%<\/strong>!<\/p>\n

\u00a0Percentage Increase\/Decrease Formula<\/strong><\/h3>\n

Increase\/Decrease=(Change\u00a0in\u00a0ValueOriginal\u00a0Value)\u00d7100\\text{Increase\/Decrease} = \\left(\\frac{\\text{Change in Value}}{\\text{Original Value}}\\right) \\times 100<\/span>Increase\/Decrease<\/span><\/span>=<\/span><\/span>(<\/span><\/span>Original\u00a0Value<\/span>Change\u00a0in\u00a0Value<\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>\u00d7<\/span><\/span>100<\/span><\/span><\/span><\/span><\/span><\/p>\n

Example:<\/strong> If the price of a mobile increases from \u20b92000 to \u20b92500, what is the percentage increase?<\/p>\n

(2500\u221220002000)\u00d7100=(5002000)\u00d7100=25%\\left(\\frac{2500 – 2000}{2000}\\right) \\times 100 = \\left(\\frac{500}{2000}\\right) \\times 100 = 25\\%<\/span>(<\/span><\/span>20002500\u2212<\/span>2000<\/span>\u200b<\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>\u00d7<\/span><\/span>100<\/span>=<\/span><\/span>(<\/span><\/span>2000500<\/span>\u200b<\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>\u00d7<\/span><\/span>100<\/span>=<\/span><\/span>25%<\/span><\/span><\/span><\/span><\/span><\/p>\n

\u00a0Shortcut Trick:<\/strong><\/h4>\n

If a value increases by “x%”, the new value =<\/strong><\/p>\n

Old\u00a0Value\u00d7(1+x100)\\text{Old Value} \\times \\left(1 + \\frac{x}{100}\\right)<\/span>Old\u00a0Value<\/span><\/span>\u00d7<\/span><\/span>(<\/span><\/span>1<\/span>+<\/span>100x<\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

If a value decreases by “x%”, the new value =<\/strong><\/p>\n

Old\u00a0Value\u00d7(1\u2212x100)\\text{Old Value} \\times \\left(1 – \\frac{x}{100}\\right)<\/span>Old\u00a0Value<\/span><\/span>\u00d7<\/span><\/span>(<\/span><\/span>1<\/span>\u2212<\/span>100x<\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

Example:<\/strong> If a \u20b9500 product increases by 20%<\/strong>, the new price =<\/p>\n

500\u00d7(1+20100)=500\u00d71.2=600500 \\times \\left(1 + \\frac{20}{100}\\right) = 500 \\times 1.2 = 600<\/span>500<\/span>\u00d7<\/span><\/span>(<\/span><\/span>1<\/span>+<\/span>10020<\/span>\u200b<\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>=<\/span><\/span>500<\/span>\u00d7<\/span><\/span>1.2<\/span>=<\/span><\/span>600<\/span><\/span><\/span><\/span><\/span><\/p>\n

\u00a0Successive Percentage Change Formula<\/strong><\/h3>\n

When two percentage changes happen successively, use:<\/p>\n

Total\u00a0Percentage\u00a0Change=x+y+xy100\\text{Total Percentage Change} = x + y + \\frac{xy}{100}<\/span>Total\u00a0Percentage\u00a0Change<\/span><\/span>=<\/span><\/span>x<\/span>+<\/span><\/span>y<\/span>+<\/span><\/span>100x<\/span>y<\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

Example:<\/strong> A price first increases by 20%<\/strong>, then decreases by 10%<\/strong>. What is the net change?<\/p>\n

20+(\u221210)+(20\u00d7\u221210)100=20\u221210\u22122=8%20 + (-10) + \\frac{(20 \\times -10)}{100} = 20 – 10 – 2 = 8\\%<\/span>20<\/span>+<\/span><\/span>(<\/span>\u2212<\/span>10<\/span>)<\/span>+<\/span><\/span>100(<\/span>20\u00d7<\/span>\u221210)<\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>20<\/span>\u2212<\/span><\/span>10<\/span>\u2212<\/span><\/span>2<\/span>=<\/span><\/span>8%<\/span><\/span><\/span><\/span><\/span><\/p>\n

Final answer:<\/strong> 8% increase<\/strong><\/p>\n

\u00a0Finding Population Growth or Depreciation<\/strong><\/h3>\n

If the population increases\/decreases by r% per year<\/strong>, the population after n years<\/strong> is:<\/p>\n

P=P0\u00d7(1+r100)nP = P_0 \\times \\left(1 + \\frac{r}{100}\\right)^n<\/span>P<\/span>=<\/span><\/span>P<\/span>0<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>(<\/span><\/span>1<\/span>+<\/span>100r<\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

Example:<\/strong> If a town has 10,000<\/strong> people and grows by 5% per year<\/strong>, what will be the population after 3 years<\/strong>?<\/p>\n

P=10000\u00d7(1+5100)3P = 10000 \\times \\left(1 + \\frac{5}{100}\\right)^3<\/span>P<\/span>=<\/span><\/span>10000<\/span>\u00d7<\/span><\/span>(<\/span><\/span>1<\/span>+<\/span>1005<\/span>\u200b<\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> =10000\u00d7(1.157)=11,570= 10000 \\times (1.157) = 11,570<\/span>=<\/span><\/span>10000<\/span>\u00d7<\/span><\/span>(<\/span>1.157<\/span>)<\/span>=<\/span><\/span>11<\/span>,<\/span>570<\/span><\/span><\/span><\/span><\/span><\/p>\n

Final Answer:<\/strong> 11,570 people<\/strong><\/p>\n

\u00a0Fastest Way to Find % of Any Number (Vedic Trick)<\/strong><\/h3>\n

\u00a0Trick for Finding 10%, 5%, 1% Fast<\/strong><\/h3>\n

10% of a number<\/strong> \u2192 Move one decimal left<\/strong>.
5% of a number<\/strong> \u2192 Take half of 10%<\/strong>.
1% of a number<\/strong> \u2192 Move two decimals left<\/strong>.<\/p>\n

Example:<\/strong> Find 7% of 320.
1% of 320<\/strong> = 3.2
7% = 3.2 \u00d7 7<\/strong> = 22.4<\/strong><\/p>\n

\u00a0Done in seconds<\/strong> without a calculator!<\/p>\n

\u00a0Shortcut for Percentage to Ratio Conversion<\/strong><\/h3>\n

Formula:<\/strong><\/p>\n

Percentage=Ratio\u00a0NumeratorRatio\u00a0Denominator\u00d7100\\text{Percentage} = \\frac{\\text{Ratio Numerator}}{\\text{Ratio Denominator}} \\times 100<\/span>Percentage<\/span><\/span>=<\/span><\/span>Ratio\u00a0Denominator<\/span>Ratio\u00a0Numerator<\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>100<\/span><\/span><\/span><\/span><\/span><\/p>\n

Examples:<\/strong><\/p>\n