Ratio and Proportion: Concepts and Formulas for Placement Aptitude
What is a Ratio?
- A ratio is a way to compare two or more quantities.
- It tells us how much of one thing there is compared to another.
- Example: If there are 2 apples and 3 oranges, the ratio of apples to oranges is 2:3.
Rule 1: If we multiply or divide the numerator and denominator of a ratio by the same number, the ratio remains unchanged.
$\frac{a}{b} =\frac{ma}{mb} \ =\frac{a/m}{b/m}$
Q: John and Abhi have their salaries in the proportion 3:5. If both of them get a hike of 20%, what is the new ratio of their salaries?
Sol: Ratio will remain unchanged. one way to visualize this is to say, their salaries are 300 and 500. Now with increase ratio of their new salaries will be $= \frac{1.2*300}{1.2*500} = 3/5$
Rule 2: If a/b = c/d = e/f = g/f = k then, $k = \frac{a+c+e+g}{b+d+f+h}$
Q: If a/b = c/d = e/f = 4 then, what is the value of $\frac{a+2c+3e}{b+2d+3f}$
Sol: Question has smartly combined Point 1 and Point 2
By Point 1; we can say a/b = c/d = 2c/2d = e/f = 3e/3f = 4
By point 2; we can say $\frac{a+2c+3e}{b+2d+3f} = 4$
What is Proportion?
- Proportion shows that two ratios are equal.
- If two ratios are the same, they are in proportion.
$\frac{a}{b} = \frac{c}{d} \ \rightarrow \ a:b :: c:d$
Rule 3: If four quantities a, b, c and d are in proportion, then following will also be true: $a*d = b*c$
Rule 4 (Componendo Dividendo): If four quantities a, b, c and d are in proportion, then following will also be true: $\ \Longrightarrow \ \frac{a+b}{a-b} =\frac{c+d}{c-d}$
Note: For aptitude, you will just need to focus on use and understanding of ratios in word problems, rather than stand alone rules. Let’s take some examples.
Q: A recipe for lemonade calls for 4 cups of lemon juice and 10 cups of water. What is the ratio of lemon juice to water?
Sol: The ratio of lemon juice to water is 4:10 = 2:5
Q: 4 notebooks cost ₹80. How much will 7 notebooks cost?
Sol: Let the cost of 7 notebooks be $x$. Set up the proportion: $\frac{4}{80} = \frac{7}{x}$
Cross-multiply: $4x=80×7=560$
$x=560/4=₹140$
Q John and Mark share money in the ratio 3:2. If they have ₹500 in total, how much does each get?
Sol: The total parts of the ratio are 3+2=5
John gets $\frac{3}{5} \times 500 = ₹300$
Mark gets $\frac{2}{5} \times 500 = ₹200$
Q: If ratio of Arin’s score to Benny’s score is 3:5. Also ratio of Benny’s score to Chandra’s score is 7:9. Then what is the ratio of score between Arin to Chandra?
Sol: $ a:b = 3:5$ and $b:c = 7:9$
Let’s convert b’s ratio term to a common term so that we can work with it later
LCM of 5 and 7 = 35
Let’s convert the ratios accordingly
$ \Longrightarrow \ a:b = 3:5 = 3*7:5*7 = 21:35$ and
$b:c = 7:9 = 7*5:9*5 = 35:45$
$ \Longrightarrow \ a:b:c = 21:35:45$
$ \Longrightarrow \ a:c = 21:45 = 7:15$
You can refer to following videos for further understanding and added perspective:
Refer Topic: Profit, Loss and Partnership: https://www.learntheta.com/placement-aptitude-profit-loss-partnership/
Read more about LearnTheta’s AI Practice Platform: https://www.learntheta.com/placement-aptitude/