**Ratio and Proportion Questions PDF: **Profit and Loss Question PDF for SSC, Railway Exam. Welcome to the **Dream Big Institution** online Free PDF section. As we all know in many competitive exams like SSC, Railways, Banking, FCI, CWC, Insurance Exams, UPSC, and other state PCS exams, Ratio and Proportion Questions asked repeatedly, so you cannot ignore the Ratio and Proportion section of Quantitative Aptitude.

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**Ratio and Proportion Definition**

The **definition of ratio and proportion** is depicted here right now. The two concepts are a significant piece of Mathematics. All things considered, additionally, you may discover a lot of examples, for example, the pace (separation/time) or value (rupees/meter) of a material, and so on, where the concept of the ratio is featured. Download Ratio and Proportion Questions PDF Given Below

Proportion is a condition that characterizes that the two given ratios are comparable to one another. For example, the time taken via train to cover 100km every hour is equivalent to the time taken by it to cover the separation of 500km for 5 hours. For example, 100km/hr = 500km/5hrs = 100km/hr.

**Ratio and Proportion Question Formula**

Now, let us learn the Maths ratio and proportion formulas here. Assume that, we have two quantities or two numbers or two entities and we have to find the ratio of these two, then the formula for ratio is defined as;

**a: b ⇒ a/b**

where a and b could be any two quantities.

Here, “a” is called the first term or antecedent, and “b” is called the second term or consequent.

* Also, read:* Ratio Formula

Now, let us assume that, in proportion, the two ratios are **a:b** & **c:d. **The two terms **‘b’** and **‘c’** are called **‘means or mean term,’** whereas the terms **‘a’** and**’** are known as ‘**extremes or extreme terms.’**

a/b = c/d or a : b :: c : d |

Let us consider one more example of a number of students in a classroom. Our first ratio of the number of girls to boys is 3:5 and that of the other is 4:8, then the proportion can be written as

3 : 5 :: 4 : 8 or 3/5 = 4/8

Here 3 & 8 are the extremes, while 5 & 4 are the means.

* Note:* The ratio value does not affect when the same non-zero number is multiplied or divided on each term.

**Ratio and Proportion Question Tricks**

Let us learn here some rules and tricks to solve problems based on ratio and proportion topic.

- If u/v = x/y, then uy = vx
- If u/v = x/y, then u/x = v/y
- If u/v = x/y, then v/u = y/x
- If u/v = x/y, then (u+v)/v = (x+y)/y
- If u/v = x/y, then (u-v)/v = (x-y)/y
- If u/v = x/y, then (u+v)/ (u-v) = (x+y)/(x-y), which is known as componendo -Dividendo Rule
- If u/v = v/x, then u/x = u
^{2}/v^{2} - If u/v = x/y, then u = x and v =y
- If a/(b+c) = b/(c+a) = c/(a+b) and a+b+ c ≠0, then a =b = c

**Ratio and Proportion Questions**

### Question. 1.

**In a mixture of 40 litres, the ratio of milk and water is 4:1. How much water must be added to this mixture so that the ratio of milk and water becomes 2:3.**

(a) 20 litres

(b) 32 litres

(c) 40 litres

(d) 30 litres

### Question. 2.

**If three numbers are in the ratio of 1:2:3 and half the sum is 18, then the ratio of squares of the numbers is:**

(a) 6: 12: 13

(b) 1: 2: 4

(c) 36: 144: 324

(d) None of these

### Question. 3.

**The ratio between the two numbers is 3:4 and their LCM is 180. The first number is:**

(a) 60

(b) 45

(c) 15

(d) 20

### Question. 4.

**The incomes of A and B are in the ratio 3:2 and their expenditures are in the ratio 5:3. If each saves Rs. 1000, then, A’s income is**

(a) Rs. 3000

(b) Rs. 4000

(c) Rs. 6000

(d) Rs. 9000

### Question. 5.

**The students in three batches at Made Easy are in the ratio 2 : 3 : 5. If 20 students are increased in each batch, the ratio change to 4:5:7. The total number of students in the three batches before the increase were.**

(a) 10

(b) 90

(c) 100

(d) 150

### Question. 6.

**The difference between the two positive numbers is 10 and the ratio between them is 5:3. Find the product the two numbers**

(a) 375

(b) 175

(c) 275

(d) 125

### Question. 7.

**Four numbers in the ratio 1:3:4:7 add up to give a sum of 105. Find the value of the biggest number**

(a) 42

(b) 35

(c) 49

(d) 63

### Question. 8.

**If Rs. 58 is divided among 150 children such that each girl and each boy gets 25 p and 50 p respectively. Then how many girls are there?**

(a) 52

(b) 54

(c) 68

(d) 62

**Solutions:**

#### Ans 1. (c)

SolutionsLet water is x

4 x : x = milk : water

32: 8 = 4x : x (since total 40 liters)

#### Ans 2.(c)

Let numbers are

x : 2x : 3x also it is given that6x = 36, x = 6

6 : 12 : 18

The ratio of squares 36: 144 : 324: or also 1 : 4 : 9

#### Ans 3. (b)

Let number are 3x and 4x

3x 4x =HCF ✕ 180

Clearly, HCF will be x

12x² = x 180, x = 15

Number will be 45:60

Note: if there are two number

#### Ans 4.(c)

Let incomes are 3x:2x

Expenditures are 5y:3y

Then

3x–5y = 1000 …..(i) also

2x–3y = 1000 …..(ii)

from (i) and (ii) we get

6x-10y = 2000

+6x-9y = 3000

-y =-1000

y=1000, x= 2000

A’s income is 6000

#### Ans 5.(c)

let students are 2x: 3r: 5x now According to the given condition

2x+20 : 3x+20 : 5x + 20 = 4 : 5 : 7

x = 10

20:30:50 = 2:3:5 and after adding 20

40:50:70

#### Ans 6. (a)

x-y = 10 ……(i)

x:y = 5:3 ……(ii)

x:y = 5t:3t ……(iii)

according to (i) and (iii)

5t-3t = 10

2t = 10, t = 5

x = 25, y = 15

Product of two numbers = 375

#### Ans 7.(c)

x : 3x : 4x : 7x

re four numbers also

x + 3x + 4x + 7x = 105

15x = 105, x = 7, 7r = 49

#### Ans 8.(c)

Let the number of girls and boys are x and y then

0.25x + 0.5 = 58 ….(i)

also

x + y = 150 ….(ii)

from (i) and (ii) we get

0.5x + y = 116

x + y = 150

So, 0.5x = 34, x = 68, y = 82

**FAQ on Ratio and Proportion Questions**

### Q. What is an example of a ratio and a proportion?

Ans: A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, **if there is 1 boy and 3 girls you could write the ratio as:** **1 : 3 (for every one boy there are 3 girls)**

### Q. What is the basic formula for ratio?

Ans: The formula for ratio is expressed as **a : b ⇒ a/b**, where, a = the first term or antecedent. b = the second term or consequent.