{"id":4177,"date":"2025-06-06T14:20:27","date_gmt":"2025-06-06T14:20:27","guid":{"rendered":"https:\/\/diznr.com\/?p=4177"},"modified":"2025-06-06T14:20:27","modified_gmt":"2025-06-06T14:20:27","slug":"mathematics-short-tricks-math-ratio-proportion-and","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/mathematics-short-tricks-math-ratio-proportion-and\/","title":{"rendered":"Mathematics Short Tricks\/ MATH RATIO AND PROPORTION"},"content":{"rendered":"

Mathematics Short Tricks\/ MATH RATIO AND PROPORTION<\/p>\n

[fvplayer id=”643″]<\/p>\n

\u00a0Mathematics Short Tricks \u2013 Ratio & Proportion<\/strong><\/h3>\n

Ratio and Proportion are essential topics for competitive exams like SSC, Banking, GATE, CAT, etc.<\/strong> Here are some quick tricks & formulas<\/strong> to solve ratio and proportion problems FAST!<\/p>\n

\u00a0What is Ratio?<\/strong><\/h3>\n

A ratio<\/strong> compares two quantities and is written as:<\/p>\n

Ratio=a:b\\text{Ratio} = a:b<\/span>Ratio<\/span><\/span>=<\/span><\/span>a<\/span>:<\/span><\/span>b<\/span><\/span><\/span><\/span><\/span><\/p>\n

Example:<\/strong> If a class has 20 boys<\/strong> and 30 girls<\/strong>, the ratio of boys to girls is:<\/p>\n

20:30=2:320:30 = 2:3<\/span>20<\/span>:<\/span><\/span>30<\/span>=<\/span><\/span>2<\/span>:<\/span><\/span>3<\/span><\/span><\/span><\/span><\/span><\/p>\n

\u00a0Always simplify ratios by dividing by the HCF<\/strong> of both terms.<\/p>\n

\u00a0What is Proportion?<\/strong><\/h3>\n

A proportion states that two ratios are equal<\/strong>:<\/p>\n

a:b=c:da:b = c:d<\/span>a<\/span>:<\/span><\/span>b<\/span>=<\/span><\/span>c<\/span>:<\/span><\/span>d<\/span><\/span><\/span><\/span><\/span><\/p>\n

Here, b & c are mean terms<\/strong>, and a & d are extreme terms<\/strong>.<\/p>\n

Product\u00a0of\u00a0Means=Product\u00a0of\u00a0Extremes\\text{Product of Means} = \\text{Product of Extremes}<\/span>Product\u00a0of\u00a0Means<\/span><\/span>=<\/span><\/span>Product\u00a0of\u00a0Extremes<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

Example:<\/strong> Find x<\/strong> if 2:5=6:x2:5 = 6:x<\/span>2<\/span>:<\/span><\/span>5<\/span>=<\/span><\/span>6<\/span>:<\/span><\/span>x<\/span><\/span><\/span><\/span>.<\/p>\n

2\u00d7x=5\u00d762 \\times x = 5 \\times 6<\/span>2<\/span>\u00d7<\/span><\/span>x<\/span>=<\/span><\/span>5<\/span>\u00d7<\/span><\/span>6<\/span><\/span><\/span><\/span><\/span> x=302=15x = \\frac{30}{2} = 15<\/span>x<\/span>=<\/span><\/span>230<\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>15<\/span><\/span><\/span><\/span><\/span><\/p>\n

Final Answer:<\/strong> x=15x = 15<\/span>x<\/span>=<\/span><\/span>15<\/span><\/span><\/span><\/span><\/p>\n

\u00a0Trick to Solve Problems Faster<\/strong><\/h3>\n

\u00a0Ratio Multiplication Trick<\/strong><\/h3>\n

If two ratios are given:<\/p>\n

a:bandc:da:b \\quad \\text{and} \\quad c:d<\/span>a<\/span>:<\/span><\/span>b<\/span>and<\/span><\/span>c<\/span>:<\/span><\/span>d<\/span><\/span><\/span><\/span><\/span><\/p>\n

To combine them into a single ratio:<\/p>\n

(a\u00d7c):(b\u00d7d)(a \\times c) : (b \\times d)<\/span>(<\/span>a<\/span>\u00d7<\/span><\/span>c<\/span>)<\/span>:<\/span><\/span>(<\/span>b<\/span>\u00d7<\/span><\/span>d<\/span>)<\/span><\/span><\/span><\/span><\/span><\/p>\n

Example:<\/strong> Find the combined ratio of 2:3<\/strong> and 4:5<\/strong>.<\/p>\n

(2\u00d74):(3\u00d75)=8:15(2 \\times 4) : (3 \\times 5) = 8:15<\/span>(<\/span>2<\/span>\u00d7<\/span><\/span>4<\/span>)<\/span>:<\/span><\/span>(<\/span>3<\/span>\u00d7<\/span><\/span>5<\/span>)<\/span>=<\/span><\/span>8<\/span>:<\/span><\/span>15<\/span><\/span><\/span><\/span><\/span><\/p>\n

Final Answer:<\/strong> 8:158:15<\/span>8<\/span>:<\/span><\/span>15<\/span><\/span><\/span><\/span><\/p>\n

\u00a0Trick for Finding a Number Based on Ratio<\/strong><\/h3>\n

If x:y = m:n<\/strong>, then:<\/p>\n

x=mm+n\u00d7Totalx = \\frac{m}{m+n} \\times \\text{Total}<\/span>x<\/span>=<\/span><\/span>m<\/span>+<\/span>n<\/span>m<\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>Total<\/span><\/span><\/span><\/span><\/span><\/span> y=nm+n\u00d7Totaly = \\frac{n}{m+n} \\times \\text{Total}<\/span>y<\/span>=<\/span><\/span>m<\/span>+<\/span>n<\/span>n<\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>Total<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

Example:<\/strong> The ratio of A’s & B\u2019s salary is 2:3<\/strong>, and their total salary is \u20b95000. Find A’s and B’s salary.<\/p>\n

A=22+3\u00d75000=25\u00d75000=2000A = \\frac{2}{2+3} \\times 5000 = \\frac{2}{5} \\times 5000 = 2000<\/span>A<\/span>=<\/span><\/span>2+<\/span>32<\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>5000<\/span>=<\/span><\/span>52<\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>5000<\/span>=<\/span><\/span>2000<\/span><\/span><\/span><\/span><\/span> B=35\u00d75000=3000B = \\frac{3}{5} \\times 5000 = 3000<\/span>B<\/span>=<\/span><\/span>53<\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>5000<\/span>=<\/span><\/span>3000<\/span><\/span><\/span><\/span><\/span><\/p>\n

Final Answer:<\/strong> A = \u20b92000, B = \u20b93000<\/p>\n

\u00a0How to Divide an Amount in a Given Ratio?<\/strong><\/h3>\n

To divide \u20b9X<\/strong> in the ratio a:ba:b<\/span>a<\/span>:<\/span><\/span>b<\/span><\/span><\/span><\/span>, use:<\/p>\n

First\u00a0part=aa+b\u00d7X\\text{First part} = \\frac{a}{a+b} \\times X<\/span>First\u00a0part<\/span><\/span>=<\/span><\/span>a<\/span>+<\/span>b<\/span>a<\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>X<\/span><\/span><\/span><\/span><\/span> Second\u00a0part=ba+b\u00d7X\\text{Second part} = \\frac{b}{a+b} \\times X<\/span>Second\u00a0part<\/span><\/span>=<\/span><\/span>a<\/span>+<\/span>b<\/span>b<\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>X<\/span><\/span><\/span><\/span><\/span><\/p>\n

Example:<\/strong> \u20b91000 is divided in the ratio 3:2.<\/p>\n

First\u00a0part=33+2\u00d71000=35\u00d71000=600\\text{First part} = \\frac{3}{3+2} \\times 1000 = \\frac{3}{5} \\times 1000 = 600<\/span>First\u00a0part<\/span><\/span>=<\/span><\/span>3+<\/span>23<\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>1000<\/span>=<\/span><\/span>53<\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>1000<\/span>=<\/span><\/span>600<\/span><\/span><\/span><\/span><\/span> Second\u00a0part=25\u00d71000=400\\text{Second part} = \\frac{2}{5} \\times 1000 = 400<\/span>Second\u00a0part<\/span><\/span>=<\/span><\/span>52<\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>1000<\/span>=<\/span><\/span>400<\/span><\/span><\/span><\/span><\/span><\/p>\n

Final Answer:<\/strong> \u20b9600 and \u20b9400<\/p>\n

\u00a0Finding the New Ratio After an Increase\/Decrease<\/strong><\/h3>\n

If two quantities are increased\/decreased by x% and y%<\/strong>, the new ratio is:<\/p>\n

New\u00a0Ratio=(a\u00d7(100+x)):(b\u00d7(100+y))\\text{New Ratio} = (a \\times (100 + x)) : (b \\times (100 + y))<\/span>New\u00a0Ratio<\/span><\/span>=<\/span><\/span>(<\/span>a<\/span>\u00d7<\/span><\/span>(<\/span>100<\/span>+<\/span><\/span>x<\/span>))<\/span>:<\/span><\/span>(<\/span>b<\/span>\u00d7<\/span><\/span>(<\/span>100<\/span>+<\/span><\/span>y<\/span>))<\/span><\/span><\/span><\/span><\/span><\/p>\n

Example:<\/strong> The ratio of A\u2019s and B\u2019s salary is 4:5. If both are increased by 20%<\/strong> and 10%<\/strong>, find the new ratio.<\/p>\n

New\u00a0Ratio=(4\u00d7120):(5\u00d7110)=480:550\\text{New Ratio} = (4 \\times 120) : (5 \\times 110) = 480 : 550<\/span>New\u00a0Ratio<\/span><\/span>=<\/span><\/span>(<\/span>4<\/span>\u00d7<\/span><\/span>120<\/span>)<\/span>:<\/span><\/span>(<\/span>5<\/span>\u00d7<\/span><\/span>110<\/span>)<\/span>=<\/span><\/span>480<\/span>:<\/span><\/span>550<\/span><\/span><\/span><\/span><\/span><\/p>\n

Simplify:<\/p>\n

24:27.524: 27.5<\/span>24<\/span>:<\/span><\/span>27.5<\/span><\/span><\/span><\/span><\/span><\/p>\n

Multiply by 2<\/strong> to remove decimals:<\/p>\n

48:5548:55<\/span>48<\/span>:<\/span><\/span>55<\/span><\/span><\/span><\/span><\/span><\/p>\n

Final Answer:<\/strong> 48:55<\/strong><\/p>\n

\u00a0Quickest Way to Compare Two Ratios<\/strong><\/h3>\n

To compare a:ba:b<\/span>a<\/span>:<\/span><\/span>b<\/span><\/span><\/span><\/span> and c:dc:d<\/span>c<\/span>:<\/span><\/span>d<\/span><\/span><\/span><\/span>, cross multiply<\/strong>:
\u00a0If a\u00d7d>b\u00d7ca \\times d > b \\times c<\/span>a<\/span>\u00d7<\/span><\/span>d<\/span>><\/span><\/span>b<\/span>\u00d7<\/span><\/span>c<\/span><\/span><\/span><\/span> \u2192 a:ba:b<\/span>a<\/span>:<\/span><\/span>b<\/span><\/span><\/span><\/span> is greater<\/strong>
\u00a0If a\u00d7d<b\u00d7ca \\times d < b \\times c<\/span>a<\/span>\u00d7<\/span><\/span>d<\/span><<\/span><\/span>b<\/span>\u00d7<\/span><\/span>c<\/span><\/span><\/span><\/span> \u2192 c:dc:d<\/span>c<\/span>:<\/span><\/span>d<\/span><\/span><\/span><\/span> is greater<\/strong><\/p>\n

Example:<\/strong> Which is greater: 3:4 or 5:7?<\/p>\n

3\u00d77=21,4\u00d75=203 \\times 7 = 21, \\quad 4 \\times 5 = 20<\/span>3<\/span>\u00d7<\/span><\/span>7<\/span>=<\/span><\/span>21<\/span>,<\/span>4<\/span>\u00d7<\/span><\/span>5<\/span>=<\/span><\/span>20<\/span><\/span><\/span><\/span><\/span><\/p>\n

Since 21 > 20<\/strong>, 3:4 is greater<\/strong> than 5:7<\/strong>.<\/p>\n

\u00a0Mean Proportion Formula<\/strong><\/h3>\n

The mean proportion between a<\/strong> and b<\/strong> is:<\/p>\n

x=a\u00d7bx = \\sqrt{a \\times b}<\/span>x<\/span>=<\/span><\/span>a<\/span>\u00d7<\/span>b<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

Example:<\/strong> Find the mean proportion of 4 and 25.<\/p>\n

x=4\u00d725=100=10x = \\sqrt{4 \\times 25} = \\sqrt{100} = 10<\/span>x<\/span>=<\/span><\/span>4\u00d7<\/span>25<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span>=<\/span><\/span>100<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span>=<\/span><\/span>10<\/span><\/span><\/span><\/span><\/span><\/p>\n

Final Answer:<\/strong> 10<\/strong><\/p>\n

\u00a0Direct & Inverse Proportion<\/strong><\/h3>\n

\u00a0Direct Proportion (More \u2192 More, Less \u2192 Less)<\/strong><\/h3>\n

If x increases, y also increases<\/strong>, then:<\/p>\n

x1:y1=x2:y2x_1:y_1 = x_2:y_2<\/span>x<\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>:<\/span><\/span>y<\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>x<\/span>2<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>:<\/span><\/span>y<\/span>2<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

Example:<\/strong> If 5 workers do a job in 10 days, how many days for 10 workers?<\/p>\n

5:10=10:x5:10 = 10:x<\/span>5<\/span>:<\/span><\/span>10<\/span>=<\/span><\/span>10<\/span>:<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span><\/p>\n

Cross multiply:<\/p>\n

5x=10\u00d710\u21d2x=55x = 10 \\times 10 \\Rightarrow x = 5<\/span>5<\/span>x<\/span>=<\/span><\/span>10<\/span>\u00d7<\/span><\/span>10<\/span>\u21d2<\/span><\/span>x<\/span>=<\/span><\/span>5<\/span><\/span><\/span><\/span><\/span><\/p>\n

Final Answer:<\/strong> 5 days<\/strong><\/p>\n

\u00a0Inverse Proportion (More \u2192 Less, Less \u2192 More)<\/strong><\/h3>\n

If x increases, y decreases<\/strong>, then:<\/p>\n

x1\u00d7y1=x2\u00d7y2x_1 \\times y_1 = x_2 \\times y_2<\/span>x<\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>y<\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>x<\/span>2<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>y<\/span>2<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

Example:<\/strong> If 8 men finish work in 12 days, how long will 16 men take?<\/p>\n

8\u00d712=16\u00d7x8 \\times 12 = 16 \\times x<\/span>8<\/span>\u00d7<\/span><\/span>12<\/span>=<\/span><\/span>16<\/span>\u00d7<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> x=8\u00d71216=6\u00a0daysx = \\frac{8 \\times 12}{16} = 6 \\text{ days}<\/span>x<\/span>=<\/span><\/span>168\u00d7<\/span>12<\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>6<\/span>\u00a0days<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

Final Answer:<\/strong> 6 days<\/strong><\/p>\n

\u00a0Summary of Tricks\u00a0<\/strong><\/h3>\n

\u00a0Memorize basic ratio concepts<\/strong>
\u00a0Use cross multiplication<\/strong> to compare ratios
\u00a0Apply direct & inverse proportion rules<\/strong>
\u00a0Use proportion formula for quick calculations<\/strong>
\u00a0Use multiplication tricks<\/strong> to find new ratios<\/p>\n

Master these tricks and solve any Ratio & Proportion question in seconds!<\/strong><\/p>\n

Would you like practice questions or PDFs for revision?<\/strong><\/p>\n

Mathematics Short Tricks\/ MATH RATIO AND PROPORTION<\/a><\/h3>\n

Ratio and Proportion: Concepts, Solved Examples, & …<\/a><\/h3>\n

QUALITATIVE APTITUDE TRICKS & SHORTCUTS FOR<\/a><\/h3>\n

RATIO AND PROPORTION.pmd<\/a><\/h3>\n

Certainly! Mastering Ratio and Proportion<\/strong> is crucial for excelling in competitive exams like GATE, SSC, Banking, and others. Below are some effective tricks and shortcuts to enhance your problem-solving speed and accuracy.<\/p>\n

\n

\ud83d\udcd8 Key Concepts<\/strong><\/h3>\n
    \n
  • Ratio<\/strong>: A comparison between two quantities, expressed as a : b<\/code>.<\/li>\n
  • Proportion<\/strong>: An equation stating that two ratios are equal, denoted as a : b :: c : d<\/code>.(GeeksforGeeks, BYJU’S)<\/li>\n<\/ul>\n
    \n

    \u26a1 Essential Tricks and Shortcuts<\/strong><\/h3>\n
      \n
    1. Mean Proportion<\/strong>:\n
        \n
      • If a : x = x : b<\/code>, then x = \u221a(a \u00d7 b)<\/code>.<\/li>\n
      • Example<\/em>: Find the mean proportion between 4 and 9.\n
          \n
        • x = \u221a(4 \u00d7 9) = \u221a36 = 6<\/code><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n
        • Third Proportion<\/strong>:\n
            \n
          • If a : b = b : c<\/code>, then c = b\u00b2 \/ a<\/code>.<\/li>\n
          • Example<\/em>: Find the third proportion to 4 and 8.\n
              \n
            • c = 8\u00b2 \/ 4 = 64 \/ 4 = 16<\/code><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n
            • Fourth Proportion<\/strong>:\n
                \n
              • If a : b = c : d<\/code>, then d = (b \u00d7 c) \/ a<\/code>.<\/li>\n
              • Example<\/em>: Find the fourth proportion to 3, 9, and 12.\n
                  \n
                • d = (9 \u00d7 12) \/ 3 = 108 \/ 3 = 36<\/code><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n
                • Componendo and Dividendo Rule<\/strong>:\n
                    \n
                  • If a \/ b = c \/ d<\/code>, then:\n
                      \n
                    • (a + b) \/ (a - b) = (c + d) \/ (c - d)<\/code><\/li>\n<\/ul>\n<\/li>\n
                    • Example<\/em>: If a \/ b = 3 \/ 5<\/code>, then:\n
                        \n
                      • (a + b) \/ (a - b) = (3 + 5) \/ (3 - 5) = 8 \/ (-2) = -4<\/code><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n
                      • Dividing a Quantity in a Given Ratio<\/strong>:\n
                          \n
                        • To divide amount A<\/code> in the ratio m : n<\/code>:\n
                            \n
                          • First part = (A \u00d7 m) \/ (m + n)<\/code><\/li>\n
                          • Second part = (A \u00d7 n) \/ (m + n)<\/code><\/li>\n<\/ul>\n<\/li>\n
                          • Example<\/em>: Divide 1800 in the ratio 2:3.\n
                              \n
                            • First part = (1800 \u00d7 2) \/ (2 + 3) = 3600 \/ 5 = 720<\/code><\/li>\n
                            • Second part = 1800 - 720 = 1080<\/code><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n
                            • Comparison of Ratios<\/strong>:\n
                                \n
                              • To compare a : b<\/code> and c : d<\/code>, convert both to fractions:\n
                                  \n
                                • a \/ b<\/code> and c \/ d<\/code><\/li>\n<\/ul>\n<\/li>\n
                                • Compare the decimal values.<\/li>\n
                                • Example<\/em>: Compare 3:4 and 5:7.\n
                                    \n
                                  • 3\/4 = 0.75<\/code>, 5\/7 \u2248 0.714<\/code><\/li>\n
                                  • Since 0.75 > 0.714, 3:4 > 5:7<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n
                                  • Compound Ratio<\/strong>:\n
                                      \n
                                    • The compound ratio of a : b<\/code> and c : d<\/code> is (a \u00d7 c) : (b \u00d7 d)<\/code>.<\/li>\n
                                    • Example<\/em>: Find the compound ratio of 2:3 and 4:5.\n
                                        \n
                                      • (2 \u00d7 4) : (3 \u00d7 5) = 8 : 15<\/code><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n
                                      • Duplicate, Triplicate, and Sub-Duplicate Ratios<\/strong>:\n
                                          \n
                                        • Duplicate Ratio<\/strong>: (a\u00b2 : b\u00b2)<\/code><\/li>\n
                                        • Triplicate Ratio<\/strong>: (a\u00b3 : b\u00b3)<\/code><\/li>\n
                                        • Sub-Duplicate Ratio<\/strong>: (\u221aa : \u221ab)<\/code><\/li>\n
                                        • Example<\/em>: For 3:4:\n
                                            \n
                                          • Duplicate: 9:16<\/code><\/li>\n
                                          • Triplicate: 27:64<\/code><\/li>\n
                                          • Sub-Duplicate: \u221a3:\u221a4 \u2248 1.732:2<\/code><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n
                                            \n

                                            \ud83d\udcda Recommended Resources<\/strong><\/h3>\n
                                              \n
                                            • Guidely<\/strong>: Offers a comprehensive PDF on ratio and proportion tricks tailored for bank exams. (CareerRide, GeeksforGeeks, Guidely)<\/li>\n
                                            • GeeksforGeeks<\/strong>: Provides detailed explanations and examples on ratios and proportions. (Scribd)<\/li>\n
                                            • BYJU’S<\/strong>: Covers definitions, formulas, and solved examples to strengthen your understanding.<\/li>\n<\/ul>\n
                                              \n

                                              \ud83c\udfa5 Video Tutorials<\/strong><\/h3>\n

                                              For visual learners, the following video tutorials can be immensely helpful:<\/p>\n

                                              Ratio and Proportion – Shortcuts & Tricks for Placement Tests<\/p>\n

                                              Ratio and Proportion – Shortcut Tricks to Solve<\/p>\n

                                              Ratio and Proportion Word Problems – Math<\/p>\n

                                              \n

                                              Feel free to reach out if you need further clarification or additional practice problems on any of these topics!<\/p>\n","protected":false},"excerpt":{"rendered":"

                                              Mathematics Short Tricks\/ MATH RATIO AND PROPORTION [fvplayer id=”643″] \u00a0Mathematics Short Tricks \u2013 Ratio & Proportion Ratio and Proportion are essential topics for competitive exams like SSC, Banking, GATE, CAT, etc. Here are some quick tricks & formulas to solve ratio and proportion problems FAST! \u00a0What is Ratio? A ratio compares two quantities and is […]<\/p>\n","protected":false},"author":64,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[83],"tags":[],"class_list":["post-4177","post","type-post","status-publish","format-standard","hentry","category-mathematics-short-tricks"],"_links":{"self":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/4177","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/users\/64"}],"replies":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/comments?post=4177"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/4177\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/media?parent=4177"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/categories?post=4177"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/tags?post=4177"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}