SSC Questions on Ratio and Proportion PDF

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SSC Questions on Ratio and Proportion PDF
SSC Questions on Ratio and Proportion PDF

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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