**$\operatorname{Ex} 3.3$
Question 1 .**

Fill in the boxes

(i) $3: 5:: \square: 20$

(ii) $\square: 24:: 3: 8$

(iii) $5: \square:: 10: 8:: 15:$

(iv) $12: \square=\square: 4=8: 16$

Solution:

(i) 12

Hint:

$5 x-3 \times 20 \rightarrow x-12$

(ii) 9

$8 x=24 \times 3 \Rightarrow x=9$

(iii) 4,12

Hint:

$10 x=8 \times 5=40 \Rightarrow x=4$

$10 \mathrm{y}=8 \times 15=120 \Rightarrow \mathrm{y}=12$

(iv) 24,2

Hint:

$16 y=8 \times 4 \Rightarrow y=2$ $12 \times 4=2 x \Rightarrow x=24$

**Question 2 .**

Say True or False.

(i) $2: 7:: 14: 4$

(ii) 7 Persons is to 49 Persons as $11 \mathrm{~kg}$ is to $88 \mathrm{~kg}$.

(iii) 10 books is to 15 books as 3 books is to 15 books.

Solution:

(i) False

(ii) False

(iii) False

**Question 3 .**

Using the numbers $3,9,4,12$ write two ratios that are in a proportion.

Solution:

(i) $3,9,4,12$

Here product of extremes $=3 \times 12=36$

Product of means $=9 \times 4=36$

$3: 9:: 4: 12$

(ii) Also if we take $9,3,12,4$

Product of extremes $=9 \times 4=36$

Product of means $=3 \times 12=36$

$9: 3:: 12: 4$

**Question 4 .**

Find whether $12,24,18,36$ are in order that can be expressed as two ratios that are in proportion.

Solution:

Yes, they are in proportion

$12: 24=18: 36$

$\frac{12}{24}=\frac{1}{2}$ Product of means $=24 \times 18=432$

$\frac{18}{36}=\frac{1}{2}$ Product of extremes $=12 \times 36=432$

Hence a $\times \mathrm{d}=\mathrm{b} \times \mathrm{c}$

**Question $5 .$**

Write the mean and extreme terms in the following ratios and check whether they are in proportion.

(i) 78 litres is to 130 litres and 12 bottles are to 20 bottles

(ii) 400 gm is to 50 gm and 25 rupees is to 625 rupees.

Solution:

(i) $78: 130:: 12: 20$

Extreme terms are 78 and 20 .

Mean terms are 130 and 12 .

Product of Extremes $=78 \times 20=1560$

Product of Means $-130 \times 12-1560$

Product of Extremes $=$ Product of means

It is in proportion.

(ii) $400: 50:: 25: 625$

Product of extremes $=400 \times 625=250,000$

Product of means $=50 \times 25=1250$

Here product of extremes $\neq$ product of means

$400: 50$ and $25: 625$ are not in proportion.

**Question $6 .$**

America's famous Golden Gate bridge is $6480 \mathrm{ft}$ long with $756 \mathrm{ft}$ tall towers. A model of this bridge exhibited in a fair is $60 \mathrm{ft}$ long with $7 \mathrm{ft}$ tall towers. Is the model in proportion to the original bridge?

Solution:

The ratio of Golden Gate Bridge \& Its model are $=6480: 756$

Product of extremes $=6480 \times 7=45,360$

Product of means $=756 \times 60=45,360$

Product of extremes $=$ Product of means

The model is in proportion to the ordinal bridge.

**Objective Type Questions
Question 7 .**

Which of the following ratios are in proportion?

a) $3: 5,6: 11$

(b) $2: 3,9: 6$

(c) $2: 5,10: 25$

(d) $3: 1,1: 3$

Solution:

(c) $2: 5,10: 25$

**Question $8 .$**

If the ratios formed using the numbers $2,5, x, 20$ in the same order are in proportion, then ' $x$ ' is

(a) 50

(b) 4

(c) 10

(d) 8

Solution:

(d) 8

$5 x=2 \times 20 \Rightarrow x=8$

**Question $9 .$**

If $7: 5$ is in proportion to $x: 25$, then ' $x$ ' is

(a) 27

(b) 49

(c) 35

(d) 14

Solution:

(c) 35