SSC Questions on Ratio and Proportion PDF

Download SSC CGL Ratio and Proportion Questions with answers PDF based on previous papers very useful for SSC CGL exams. Top-10 Very Important Ratio and Proportion Questions for SSC Exams.

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Question 1: If $a : b = 4 : 5$, then what will be the ratio of $\left(\frac{a}{b}\right) : \left(\frac{b}{a}\right)$?

a) 4 : 5

b) 5 : 4

c) 16 : 25

d) 1 : 1

Question 2: The ratio of two numbers is 13 : 20. If the difference between them is 189, then what is the smaller of the two numbers?

a) 279

b) 221

c) 297

d) 351

Question 3: If x : y = 5 : 4, then what will be the ratio of $\left(\frac{x}{y}\right) : \left( \frac{y}{x} \right)$?

a) 25 : 16

b) 16 : 25

c) 4 : 5

d) 5 : 4

Question 4: The ratios of spirit and water in vessels A and B are 4 : 5 and 7: 11, respectively. The contents of A and B are mixed in the ratio 2 : 5. What is the ratio of spirit and water in the resulting solution?

a) 22 : 75

b) 53 : 75

c) 17 : 25

d) 13 : 20

Question 5: The ratio of the mean proportional between 0.7 and 2.8 and the third proportional to 2.5 and 3.5 is:

a) 7 : 2

b) 2 : 7

c) 7 : 3

d) 3 : 7

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Question 6: The third proportional of two numbers 4 and 28 is _______.

a) 52

b) 56

c) 84

d) 196

Question 7: Find two numbers such that their mean proportion is 8 and third proportion is 64.

a) 4 and 8

b) 8 and 16

c) 8 and 8

d) 4 and 16

Question 8: The third proportional to $(\frac{x}{y}+\frac{y}{x}) and \sqrt{x^{2}+y^{2}}$ is

a) xy

b) $\sqrt{xy}$

c) $3\sqrt{xy}$

d) $4\sqrt{xy}$

Question 9: The third proportional of two numbers 9 and 15 is

a) 21

b) 30

c) 25

d) 45

Question 10: The third proportional of two numbers 9 and 24 is

a) 39

b) 48

c) 72

d) 64

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Answers & Solutions:

1) Answer (C)

Given = $a : b = 4 : 5$

Let $a=4$ and $b=5$

To find = $\left(\frac{a}{b}\right) : \left(\frac{b}{a}\right)$

= $a^2:b^2=16:25$

=> Ans – (C)

2) Answer (D)

Let the numbers be $13x$ and $20x$

Difference = $20x-13x=7x=189$

=> $x=\frac{189}{7}=27$

Smaller number = $13\times27=351$

=> Ans – (D)

3) Answer (A)

Given = x : y = 5 : 4

Let $x=5$ and $y=4$

To find = $\left(\frac{x}{y}\right) : \left( \frac{y}{x} \right)$

= $x^2:y^2=25:16$

=> Ans – (A)

4) Answer (C)

Let quantity of mixture in A be 36 litres and in B be 90 litres (now their ratio is 2:5)

=> Spirit in mixture A = 16 litres and water = 20 litres

Similarly, spirit in mixture B = 35 litres and water = 55 litres

2 parts of A and 5 parts of B are taken, => Total spirit : total water = $(16+35):(20+55)$

= $51:75=17:25$

=> Ans – (C)

5) Answer (B)

Mean proportional between 0.7 and 2.8 = $\sqrt{0.7\times2.8}=1.4$

Let third proportional to 2.5 and 3.5 be $x$

=> $\frac{2.5}{3.5}=\frac{3.5}{x}$

=> $x=\frac{3.5\times3.5}{2.5}=4.9$

$\therefore$ Required ratio = $\frac{1.4}{4.9}=2:7$

=> Ans – (B)

6) Answer (D)

Three numbers a,b,c are in proportion iff $b^2 = ac$

Here, a = 4 and b = 28

=> $(28)^2 = 4 \times c$

=> $c = \frac{28 \times 28}{4} = 7 \times 28$

=> $c = 196$

=> Ans – (D)

7) Answer (D)

Three numbers a,b,c are in proportion iff $b^2 = ac$ where $b$ is the mean proportion and $c$ is the third proportion

Mean proportion of two numbers $x$ and $y$ = 8

=> $xy = (8)^2 = 64$ —————(i)

Third proportion = 64

=> $y^2 = x \times 64$ ————-(ii)

Substituting value of $x$ from equation(i) in equation(ii), we get :

=> $y^2 = \frac{64}{y} \times 64$

=> $y^3 = (2)^6 \times (2)^6 = (2)^{6 + 6}$

=> $y = (2)^{\frac{12}{3}} = 2^4 = 16$

Substituting it in equation(i), => $x = \frac{64}{16} = 4$

=> Ans – (D)

8) Answer (A)

Let the third proportion be x.
$(\frac{x}{y}+\frac{y}{x}) : \sqrt{x^{2}+y^{2}}$ :: $ \sqrt{x^{2}+y^{2}} : z$
$(\frac{x^2+y^2}{xy}) : \sqrt{x^{2}+y^{2}}$ :: $ \sqrt{x^{2}+y^{2}}: z$
$(\frac{\sqrt{x^2+y^2}}{xy}) : 1$ :: $\frac{ \sqrt{x^{2}+y^{2}}}{z}$
$(\frac{\sqrt{x^2+y^2}}{xy}) $ :: $\frac{ \sqrt{x^{2}+y^{2}}}{z}$
z=xy
Option A is the correct answer.

9) Answer (C)

Three numbers a,b,c are in proportion iff $b^2 = ac$ where $b$ is the mean proportion and $c$ is the third proportion

The given numbers are 9 and 15

=> $(15)^2 = 9 \times c$

=> $c = \frac{15 \times 15}{9}$

=> $c = 5 \times 5 = 25$

=> Ans – (C)

10) Answer (D)

Three numbers a,b,c are in proportion iff $b^2 = ac$ where $b$ is the mean proportion and $c$ is the third proportion

The given numbers are 9 and 24

=> $(24)^2 = 9 \times c$

=> $c = \frac{24 \times 24}{9}$

=> $c = 8 \times 8 = 64$

=> Ans – (D)

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