1 Marks 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.
$8 : x :: 48 : 18 $
$\Rightarrow 144 = 48x$ (Product of extremes = Product of means)
$\Rightarrow x = 3$

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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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MCQ 31 Mark

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

✓
$15 : 8$
B
$6 : 5$
C
$8 : 5$
D
$8 : 15$

Answer

Correct option: A.

$15 : 8$

$\text{A : B}=2:3,\text{B : C}=4:5$
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.
Suppose that the third proportional is $x$.
Then, $9: 12 :: 12 : x $
$\Rightarrow 9x = 144$ (Product of extremes = Product of means)
$\Rightarrow x = 16$

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

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

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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 $A : B = 5 : 4.$
$\frac{16}{100}\text{ A}=\frac{20}{100}\text{B}$
$\Rightarrow\frac{\text{A}}{\text{B}}=\frac{20}{16}=\frac{5}{4}$

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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 1$50 = 15 135 ÷ 15 : 150 ÷ 15$ $($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 $C : A = 15 : 8.$
$\frac{\text{A}}{\text{C}}=\frac{\text{A}}{\text{B}}\times\frac{\text{B}}{\text{C}}$
$=\frac{2}{3}\times\frac{4}{5}=\frac{8}{15}$
$\therefore\text{C : A}=15:8$

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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.
Suppose that the men proportional is $x$
Then, $0.4 : x :: x : 0.9 $
$\Rightarrow 0.9 \times 0.4 = x × x$ (Product of extremes = Product of means)
$\Rightarrow x² = 0.36 $
$\Rightarrow x = 0.6$

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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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Question 141 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 151 Mark