1 Mark Question

Question 11 Mark

Write ‘T’ for true and ‘F’ for false for the following:
If 8 : x :: 48 : 18, then x = 3.

Answer

True.
Solution:
8 : x :: 48 : 18
⇒ 144 = 48x (Product of extremes = Product of means)
⇒ x = 3

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Question 21 Mark

Express the following ratios in the simplest form:
$\frac{1}{6}:\frac{1}{9}$

Answer

$\frac{1}{6}:\frac{1}{9}$$\frac{3\ :\ 2}{18}=3 : 2$

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Question 31 Mark

Mark against the correct answer in the following:If A : B = 2 : 3 and B : C = 4 : 5, then C : A = ?

15 : 8
6 : 5
8 : 5
8 : 15

Answer

15 : 8

Solution:

$\text{A : B}=2:3,\text{B : C}=4:5$

Or $\frac{\text{A}}{\text{B}}=\frac{2}{3}$ and $\frac{\text{B}}{\text{C}}=\frac{4}{5}$

Multiplying $\frac{\text{A}}{\text{B}}\times\frac{\text{B}}{\text{C}}=\frac{2}{3}\times\frac{4}{5}$

$\Rightarrow\frac{\text{A}}{\text{C}}=\frac{8}{15}$

$\Rightarrow\frac{\text{C}}{\text{A}}=\frac{15}{8}$

$\therefore\text{C : A}=15:8$

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Question 41 Mark

Express the following ratios in the simplest form:
$4:5:\frac{9}{2}$

Answer

$4:5:\frac{9}{2}$$\frac{8\ :\ 10\ :\ 9}{2}=8:10:9$

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Question 51 Mark

Write ‘T’ for true and ‘F’ for false for the following:
The third proportional to 9 and 12 is 10.5

Answer

False.
Solution:
Suppose that the third proportional is x.
Then, 9: 12 :: 12 : x
⇒ 9x = 144 (Product of extremes = Product of means)
⇒ x = 16

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Question 61 Mark

Fill in the blank.
If A : B = 5 : 7 and B : C = 6 : 11, then A : B : C = ______.

Answer

If A : B = 5 : 7 and B : C = 6 : 11, then A : B : C = 30 : 42 : 77.
Solution:
$\frac{\text{A}}{\text{B}}=\frac{5\times6}{7\times6}=\frac{30}{47}$
$\Rightarrow\frac{\text{B}}{\text{C}}=\frac{6\times7}{11\times7}=\frac{42}{77}$
$\Rightarrow\text{A : B :}=30:42:77$

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Question 71 Mark

Write ‘T’ for true and ‘F’ for false for the following:
If (3a + 5b) : (3a - 5b) = 5 : 1, then a : b = 5 : 2.

Answer

True.
Solution:
$\frac{3\text{a}+5\text{b}}{3\text{a}-5\text{b}}=\frac{5}{1}$
$\Rightarrow3\text{a}+5\text{b}=15\text{a}=25\text{b}$
$\Rightarrow12\text{a}=30\text{b}$
$\Rightarrow\frac{\text{a}}{\text{b}}=\frac{30}{12}=\frac{5}{2}$
$\therefore\text{a : b}=5:2$

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Question 81 Mark

Fill in the blank.
If 16% of A = 20% of B, then A : B = _____.

Answer

If 16% of A = 20% of B, then A : B = 5 : 4.
Solution:
$\frac{16}{100}\text{ A}=\frac{20}{100}\text{B}$
$\Rightarrow\frac{\text{A}}{\text{B}}=\frac{20}{16}=\frac{5}{4}$

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Question 91 Mark

Express the following ratios in the simplest form:
13.5 : 15

Answer

13.5 : 15 or 135 : 150
HCF of 135 and 150 = 15
135 ÷ 15 : 150 ÷ 15 (Dividing by 15)
= 9 : 10

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Question 101 Mark

If 2: 9 :: x : 27, find the value of x.

Answer

$2:9::\text{x}:27$
$9\times\text{x}=2\times27$
$\text{x}=\frac{2\times27}{9}=2\times3=6$

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Question 111 Mark

Fill in the blank.
If A : B = 2 : 3 and B : C = 4 : 5, then C : A = ______.

Answer

If A : B = 2 : 3 and B : C = 4 : 5, then C : A = 15 : 8.
Solution:
$\frac{\text{A}}{\text{C}}=\frac{\text{A}}{\text{B}}\times\frac{\text{B}}{\text{C}}$
$=\frac{2}{3}\times\frac{4}{5}=\frac{8}{15}$
$\therefore\text{C : A}=15:8$

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Question 121 Mark

Write ‘T’ for true and ‘F’ for false for the following:
Mean proportional between 0.4 and 0.9 is .6.

Answer

True.
Solution:
Suppose that the men proportional is x
Then, 0.4 : x :: x : 0.9
⇒ 0.9 × 0.4 = x × x (Product of extremes = Product of means)
⇒ x² = 0.36
⇒ x = 0.6

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Question 131 Mark

Express the following ratios in the simplest form:
24 : 40

Answer

24 : 40
HCF of 24, 40 = 8
24 : 40 = 24 ÷ 8 : 40 ÷ 8 = 3 : 5 (Dividing by 8)

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