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Ratio and Proportion are based mainly on fractions. It is when a fraction is represented via a:b, then it is considered to be a ratio and proportion is when the two ratios are said to equal. In this case, a and b can be any two integers. The concept of ratio and proportion lays the foundation to understand the various concepts in mathematics.
The questions based on ratio and proportion range from 2 to 3 and are asked in Data Interpretation questions as well. Some of the exams in which questions based on ratio and proportion are asked include SBI PO, IBPS PO, IBPS SO, IBPS Clerk, SBI Clerk, IBPS RRB, SSC CGL, NIACL AO and LIC AAO etc.
Ratio and Proportion Questions PDF:
What are Ratio and Proportion
In certain cases, the comparison of two quantities using division is very efficient. The case where a comparison of the two quantities is made is known as a ratio. It also tells us about the number of times one quantity is equivalent to another quantity. In other words, the ratio is the number, which can be used to denote one quantity as a fraction of another.
The two numbers in a ratio can only be compared when they have the same unit. We make use of ratios to compare two things. The sign used to denote a ratio is ‘: ’.
A ratio can be expressed as a fraction. Let’s say the fraction ? and can be represented as 3 to 5.
Formula for Ratio
Let’s assume, we have two quantities or numbers, and then the formula for ratio is,
a : b ⇒ a/b
here a and b could be any two quantities.
Example: In ratio 5 : 9, is represented by 5/9, here 5 is antecedent and 9 is consequent.
Ratio Types
The type of ratios include:
1. Compounded Ratio: The compounded ratios include a : b and c : d which is the ratio of ac : bd, and that of a : b, c : d and e : f is the ratio ace : bdf.
2. Duplicate Ratio: Duplicate ratio includes the ratio a : b as the ratio of a2 : b2
3. Reciprocal Ratio: It is the reciprocal ratio of a : b which is (1/a) : (1/b) and where a≠0 and b≠0
Key Points to Remember
? The ratio can exist between the quantities of a similar kind
? In the case of comparison of two things, the units should be similar
? The comparison of two ratios can be done if the ratios are equivalent
What is Proportion
It refers to the case where two ratios are equal to each other. In other words, it denotes the equality of two fractions. In the case of proportion, where two sets of numbers are increasing or decreasing in the same ratio, then ratios are said to directly proportional.
Ratio and proportions are said to be the faces of the same coin. In the case where two ratios are equal in value, they are said to be in proportion. In simple words, it is the comparison of two ratios and is denoted using the symbol ‘ : : ’ or ‘=’.
What is Continued Proportion
Consider two ratios, a : b and c : d.
Then in this case, the continued proportion for the two terms, can be there in terms of convection to a single term. This would be the LCM of means.
For example, the LCM of b and c will be bc.
If we multiply, the first ratio by c and the second ratio by b, then we have,
ca : bc
bc : bd
In this, case the continued proportion can be written as = ca : bc : bd
Formula for Proportion
Let’s assume, the numbers to be in proportion, the two ratios are a : b & c : d. The two terms ‘b’ and ‘c’ denotes the mean term, where terms such as ‘a’ and ‘d’ are known as ‘extremes or extreme terms.’
a/b = c/d or a : b : : c : d
Properties of Proportion
The following are important properties of proportion:
Dividendo – In this case, If a : b = c : d, then a – b : b = c – d : d
Addendo - In this case, If a : b = c : d, then a + c : b + d
Subtrahendo – In this case, If a : b = c : d, then a – c : b – d
Componendo – In this case,If a : b = c : d, then a + b : b = c+d : d
Alternendo – In this case,If a : b = c : d, then a : c = b : d
Invertendo – In this case, If a : b = c : d, then b : a = d : c
Componendo and dividendo – In this case, If a : b = c : d, then a + b : a – b = c + d : c – d
What is Fourth, Third and Mean Proportional
Lets, take, a : b = c : d, then :
In this case, d is known as the fourth proportional to a, b, c.
c is known as the third proportion to a and b.
The Mean proportional of a and b is √(ab).
Duplicate Ratios
In case, a : b is in a ratio, then :
a2 : b2 is known as the duplicate ratio
√a : √b is known as the sub-duplicate ratio
a3 : b3 is known as the triplicate ratio
Examples of Ratio and Proportion
Example 1:
The total number of students in a school is 2140. If the number of girls in the school is 1200, then what is the respective ratio of the total number of boys to the total number of girls in the school?
A. 26 : 25
B. 47 : 60
C. 18 : 13
D. 31 : 79
E. None of these
Ans. B
Total No. of boys = 2140 – 1200 = 940
Respective ratio = 940 : 1200 = 47 : 60.
Hence, option B is correct.
Example 2:
Seats for Maths, English and General Knowledge are in the ratio of 5 : 7 : 8 respectively. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the respective ratio of increased seats?
A. 2 : 3 : 4
B. 6 : 7 : 8
C. 6 : 8 : 9
D. Can't be determined
E. None of these
Ans. A
| Required ratio = 5 × | 140 | : 7 × | 150 | : 8 × | 175 |
| 100 | 100 | 100 |
= 5 × 140 : 7 × 150 : 8 × 175 = 2 : 3 : 4
Hence, option A is correct.
Example 3 :
In the income statement of Asha and Ravenna, the ratio of their income in the year 2017 was 5 : 4. The ratio of Asha’s income in the year 2018 to that in 2017 is 3 : 5 and the ratio of Ravenna’s income in the year 2018 to that in 2017 is 3 : 2. If Rs. 10242 is the sum of the income of Asha and Ravenna in the year 2018, then find the income of Ravenna in the year 2017?
A. Rs. 1024
B. Rs. 1138
C. Rs. 2776
D. Rs. 2420
E. Rs. 4552
Ans. E
Let the income of Asha in 2018 and 2017 be 3x and 5x respectively.
Let the income of Ravenna in 2018 and 2017 be 3y and 2y respectively
Since, the ratio of their income in the year 2017 was 5 : 4
5x : 2y = 5 : 4
2x = y
The sum of their incomes in 2018 is Rs. 10242
3x + 3y = 10, 242
9x = 10, 242
x = 1,138 and y = 2276
Ravenna’s income for the year 2017 = 2y = Rs. 4552
Hence, option E is correct.
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