Ratio and Proportion Questions PDF for SSC, Railways and Banking Exams
Ratio and Proportion Questions PDF for SSC, Railways and Banking Exams

Quant Booster Dose – Ratio and Proportion Questions PDF

Ratio and Proportion Question PDF with Answers for government exams like SSC, Railways, Banking, FCI, CWC, Insurance Exams, UPSC, and other state PCS exams. As we all know in many competitive exams in Quantitative Aptitude/ Numerical Ability subject Ratio and Proportion Questions asked repeatedly, so you cannot ignore the Ratio and Proportion Questions PDF.

As questions are based on previous year papers, there are chances that candidates will find many questions from the Ratio and Proportion Questions with Answers PDF in all competitive Exams. If you check the last 4-5 year’s papers of SSC, Railways and Banking Exams, you will find that many different types of Ratio and Proportion questions are asked. Today we have compiled “450+ Ratio and Proportion Questions PDF with Answers for SSC, Railway & Banking Exam”. You can download Free Ratio and Proportion Questions with Solution so that you get all the important questions at one place. And it will become very easy for you guys to revise them.

Ratio and Proportion Questions PDF for SSC, Railways and Banking Exams

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Ratio and Proportion Questions with Answers | Download Free PDF

What is Ratio and Proportion?

The definition of ratio and proportion is described here in this section. Both concepts are an important part of Mathematics. In real life also, you may find a lot of examples such as the rate of speed (distance/time) or price (rupees/meter) of a material, etc, where the concept of the ratio is highlighted. Proportion is an equation that defines that the two given ratios are equivalent to each other. For example, the time taken by train to cover 100km per hour is equal to the time taken by it to cover the distance of 500km for 5 hours. Such as 100km/hr = 500km/5hrs.

Ratios are used for comparing two quantities of an identical style whereas when two or more such ratios are identical, they are declared to be in proportion.

Ratios are used when we are required to express one number as a fraction of another. If we have two quantities, say x and y, then the ratio of x to y is calculated as xyxy and is written as x:yx:y. The first term of the ratio is called antecedent and the second term is called the consequent.

Compound ratio is the ratio obtained if two or more ratios are given and the antecedent of one is multiplied by the antecedent of others and consequents are multiplied by the consequences of others. Compounded ratio of the ratios (a:b),(c:d),(e:f)willbe(ace:bdf)(a:b),(c:d),(e:f)willbe(ace:bdf)

Proportion is an equation that specifies that the two given ratios are identical to one another. We can say that the proportion states the equivalency of the two fractions or the ratios i.e Equivalent Ratios. Proportions are represented by the symbol (::)(::) or equal to (=)(=).

That is the proportion is signified by double colons. For example, ratio 6:86:8 is the same as ratio 3:43:4. This can be written as 6:8::3:46:8::3:4.

Product of means = Product of extremes

Thus, a:bc:d(b×c)=(a×d)

Tips and Tricks on Ratio and Proportion

Students can find different tips and tricks for solving questions related to ratio and proportion below:

Tip 1: In ratio, if both the antecedent and the consequent are multiplied or divided by the same number (except 0) then the ratio will remain the same.

Tip 2: If a proportion is such as a:x::x:b then x is called the mean proportional or second proportional of a and b. And if a proportion is such that a:b::b:x then x is called the third proportional of a and b.

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Ratio and proportion formula

The formula for ratio and proportion is integral for solving the ratio and proportion questions. The following is the formula used for the calculation:

Formula for ratio

A : B => a / b

The ratio is denoted by the dividend symbol when two quantities, a and b, are compared.

  • The first step is determining whether the ratio is presented in part-to-part or part-to-whole.
  • After that, calculate the parts or whole as per its requirement and put the values into the ratio.
  • If necessary, simplify the values until it comes to their lowest value. For example, if the initial ratio is 10: 30, it can be further simplified as 1 : 3, where the ratio is 1 part for every 3 parts.

Formula for proportion 

a : b :: c : d => a/b = c /d

Comparing or equating two different ratios – the above equation a: b and c : d where the proportion is shown through a double dividend (:: ) or equal sign.

  • The first step toward finding the proportion is writing the equation and putting the equivalent ratios.
  • Suppose the numeric part of one ratio is the multiple of the other ratio corresponding to it in the proportion equation. It is easy to calculate the quantity by multiplying the other part of the given ratio by the same number.
  • However, if there is no relation between the two ratios, it can be solved with the help of an unknown value by isolating the variable presenting it.

Properties of Ratio and Proportion 

The ratio consists of values compared by a dividend. The number on the left side is the antecedent, and the right side is the consequent. When multiplied or divided by the same non-zero number, the ratio remains the same. Let’s assume that in ratio and proportion, two ratios a/b and c/d, are equal, represented by the following:

(a) Invertendo represented by a/b = c/d => b/a = d/c

(b) Alternendo represented by a/b = c/d => a/c = b/d

(c ) Componendo represented by a/b = c/d => (a + b)/b = (c+d)/d

(d) Dividendo represented by a/b = c/d => (a – b)/ b = (c – d)/ d

  • In the case of proportion, when two ratios are equal, it is proportional to each other. It is presented as a product of extremes equal to the product of means.

a: b:: c : d, where a and d are the extremes and b and c are the means.

  • When a, b, c and d are placed in continued proportion, it is presented as a:b = b:c = c:d
  • For example, in the equation a:b = b:c, b is the mean proportion. Also, b2 = ac.
  • In an equation a:b = b:c, c is the considered third proportion to the numbers a and b
  • However, if there is a ratio and proportion a:b = c:d, then d is the fourth proportional to the numbers a, b and c.

Ratio and Proportion Practice Questions with Answers

1. The populations of two villages are 1525 and 2600 respectively. If the ratio of male to female population in the first village is 27 : 34 and the ratio of male to female population in the second village is 6 : 7, then what is the ratio of male to female population of these two villages taken together?

(a) 33/41

(b) 85/82

(c) 71/90

(d) 5/6

(e) None of these

Show Correct Answers

Correct Answer:  (d) 5/6

Explanation:  The populations of two villages are 1525 and 2600 respectively

The ratio of male to female population in the first village is 27 : 34

The ratio of male to female population in the second village is 6 : 7

Concept Used:

If the ratio of male and female is a : b

Then male = a/(a + b)

Calculation:

Population of 1 st village = 1525

Ratio of male to female population in the first village is 27 : 34

So,

Number of males in first village = 1525 × (27/61) = 25 × 27 = 675

Number of females in first village = 1525 – 675 = 850

And

Population of 2 nd village = 2600

Ratio of male to female population in the 2 nd village is 6 : 7

So,

Number of males in 2 nd village = 2600 × 6/13 = 200 × 6 = 1200

Number of females in 2 nd village = 2600 – 1200 = 1400

Hence,

Ratio of male to female population of these two villages taken together

= (675 + 1200) : (850 + 1400)

= 1875 : 2250

= 5 : 6

2 . A sum of money is to be distributed among A, B, C and D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 2,000 more than D, what is B’s share?

(a) Rs. 2,000

(b) Rs. 4,000

(c) Rs. 6,000

(d) Rs. 8,000

(e) None of these

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Correct Answer:  (b) Rs. 4,000

Explanation:  Sum of money is distributed among A, B, C and D in the ratio = 5: 2: 4: 3

Share of C = Rs.2000 more than D

Calculation:

Difference between ratio of C and D = 4 – 3 = 1 unit

According to question:

1 unit = Rs.2000

∴ the share of B = 2000 × 2 = 4000

∴ the required share of B = Rs.4000

3. In a school, students using school bus, bike and bicycle for transport are in the proportion 6 ∶ 3 ∶ 1. If the total strength of the school is 1200, find the number of students who use bicycle for transport. (Each student uses only one of the given 3 modes of transport)

(a) 120

(b) 180

(c) 240

(d) 100

(e) None of these

Show Correct Answers

Correct Answer:  (a) 120

Explanation:  Ratio of students using school bus, bike and bicycle = 6 : 3 : 1

Total strength of school = 1200

Concept Used:

Total Students = Ratio × Number of students using any one vehicle

Calculation:

⇒ Let the number of students using school bus, bike and bicycle be 6x, 3x and x respectively.

⇒  6x+3x+x=12006x+3x+x=1200

⇒  10x=120010x=1200

⇒  x=120x=120

⇒ Number of students who use bicycle for transport = x = 120

4. The ratio of time taken by A and B to cover a certain distance is 17 ∶ 19. Find the ratio of their respective speed.

(a) 11 ∶ 15

(b) 15 ∶ 19

(c) 17 ∶ 15

(d) 19 ∶ 17

(e) None of these

Show Correct Answers

Correct Answer:  (d) 19 ∶ 17

Explanation:  The ratio of time taken by A and B to cover a certain distance is 17 ∶ 19

Concept used :

The speed ratio is inversely proportional to the time ratio

Calculation:

As per the question,

The time ratio is 17 : 19

So, the required speed ratio will be

1/17 : 1 / 19

⇒ 19 : 17

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5. Find the fourth proportion to 55, 60 and 33.

(a) 36

(b) 24

(c) 28

(d) 30

(e) None of these

Show Correct Answers

Correct Answer:  (a) 36

Explanation:  If four number a,b,c,d are in proportion

Then we can say that

a / b = c / d

⇒ a × d  = b × c

Calculation:

Let the number be x

As per the question,

55 × x = 60  × 33

⇒ x = (60  × 33) / 55

⇒ x = 36

6. Two numbers are 30% and 20% less than a third number respectively. The ratio of first two numbers is:

(a) 7 : 6

(b) 3 : 2

(c) 7 : 8

(d) 8 : 7

(e) None of these

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Correct Answer:  (c) 7 : 8

Explanation:  Two numbers are 30% and 20% less than a third number respectively.

Formula Used:

If a number is x% less than another number, then it is equal to (100 – x)% of that number.

Ratio = First number / Second number

Calculation:

Let the third number be 100.

First number = 100 – 30% of 100

First number = 100 – 30

First number = 70

Second number = 100 – 20% of 100

Second number = 100 – 20

Second number = 80

Ratio of the first two numbers = First number / Second number

⇒ Ratio = 70 / 80

⇒ Ratio = 7 / 8

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7. The ratio of two numbers is 2 : 3 and their product is 726. The smallest number between the two numbers is:

(a) 22

(b) 55

(c) 33

(d) 11

(e) None of these

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Correct Answer:  (a) 22

Explanation:  The ratio of two numbers = 2:3

Their product = 726

Formula Used:

Let the numbers be 2x and 3x.

Product of numbers = (2x) × (3x)

Calculation:

Product of numbers = 726

⇒ (2x) × (3x) = 726

⇒ 6x2 = 726

⇒ x2 = 726 / 6

⇒ x2 = 121

⇒ x = √121

⇒ x = 11

Smallest number = 2x = 2 × 11 = 22

8. If t : u = 7 : 4, then what is the value of (7t + 4u) : (7t – 4u)?

(a) 44 : 23

(b) 23 : 45

(c) 65 : 33

(d) 46 : 25

(e) None of these

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Correct Answer:  (c) 65 : 33

Explanation:  t : u = 7 : 4

Formula Used:

(7t + 4u) : (7t – 4u)

Calculation:

Let t = 7k and u = 4k, where k is a constant.

So, 7t = 7 × 7k = 49k

4u = 4 × 4k = 16k

⇒ (7t + 4u) = 49k + 16k = 65k

⇒ (7t – 4u) = 49k – 16k = 33k

Therefore, (7t + 4u) : (7t – 4u) = 65k : 33k = 65 : 33

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9. Rs. 100 is divided in such a way between A and B such that the rupees of A : the rupees of B = 9 : 11. What are the amount of rupees of A and B?

(a) Rs. 35 and Rs. 65

(b) Rs. 45 and Rs. 55

(c) Rs. 43 and Rs. 57

(d) Rs. 39 and Rs. 61

(e) None of these

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Correct Answer:  (b) Rs. 45 and Rs. 55

Explanation:  Total amount = Rs. 100

Ratio of amounts (A : B) = 9 : 11

Formula Used:

Amount of A = (Ratio of A / Sum of Ratios) × Total Amount

Amount of B = (Ratio of B / Sum of Ratios) × Total Amount

Calculation:

Sum of Ratios = 9 + 11

Sum of Ratios = 20

Amount of A = (9 / 20) × 100

Amount of A = 9 × 5

Amount of A = 45

Amount of B = (11 / 20) × 100

Amount of B = 11 × 5

Amount of B = 55

10. u : v = 4 : 7 and v : w = 9 : 7. If u = 72, then what is the value of w?

(a) 98

(b) 77

(c) 63

(d) 49

(e) None of these

Show Correct Answers

Correct Answer:  (a) 98

Explanation:  u : v = 4 : 7 and v : w = 9 : 7

Concept Used: In this type of question, number can be calculated by using the below formulae

Calculation:

u : v = 4 : 7 and v : w = 9 : 7

To make ratio v equal in both cases

We have to multiply the 1st ratio by 9 and 2nd ratio by 7

u : v = 9 × 4 : 9 × 7 = 36 : 63 —-(i)

v : w = 9 × 7 : 7 × 7 = 63 : 49 —-(ii)

Form (i) and (ii), we can see that the ratio v is equal in both cases

So, Equating the ratios we get,

u ∶ v ∶ w = 36 ∶ 63 ∶ 49

⇒ u ∶ w = 36 ∶ 49

When u = 72,

⇒ w = 49 × 72/36 = 98

All the Ratio and Proportion questions are formulated as per the level of Bank PO exams. The Ratio and Proportion questions in this PDF has a moderate and hard level of difficulty. All the candidates who are preparing for banking exams are advised to practice all these important questions to score well in the exam. To remove any doubt or difficulty in any topic, go through the study notes of each topic from the links given above.

Why Quantitative Aptitude Ratio and Proportion Questions PDF is Important for Exams?

  • All the questions prepare by Exams experts.
  • The practice questions covered are across the levels i.e. Easy, Moderate, and Difficult.
  • Provides a detailed approach to the solution of each question.
  • Focuses on all the new patterns and advanced-level type questions.
  • Ratio and Proportion Questions PDF boosts confidence and reduces pre-exam jitters by regularly attempting a variety of questions and tackling the difficulty level expected in the final exam.

This Quant Booster Dose Ratio and Proportion Questions PDF is useful for the upcoming Banking and Insurance exams i.e. IBPS PO, SBI PO, Clerk, IBPS RRB PO & Clerk, RBI Assistant, RBI Grade B, NABARD, LIC AAO, SSC (CGL, CHSL, MTS, CPO, and Constable), Railway RRB (NTPC, Group D, JE, ALP) & Other Government Exams.

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8700+ Quantitative Aptitude Topic wise Questions and Answers – Download Free PDF

8700+ Quantitative Aptitude Topic wise Questions and Answers – Download Free PDF

Quant Booster Dose – Topic-wise Quantitative Aptitude Questions and Answers