1 Marks Question

Question 11 Mark

Which of the following statements are true?
$12 : 18 = 28 : 12$

Answer

$12 : 18 = 28 : 12$
$\frac{12}{18}=\frac{28}{12}$
$\frac{6}{9}\neq\frac{14}{6}$
False.

Question 21 Mark

Express the following ratios in language of daily life: The ratio of the number of bad pencils to that good pencils produced in a factory is $1 : 9.$

Answer

The number of bad pencils produced in a factory is $\frac{1}{9}$ of the number of good pencils produced in the factory.

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Question 31 Mark

Fill in the blanks: If $1, 2, 3$, and $x$ are in proportion, then $x =$ ..........

Answer

If $1, 2, 3,$ and $x$ are in proportion, then $x = 6. 1 : 2 : : 3 : x$
$\Rightarrow\frac{1}{2}=\frac{3}{\text{x}}$
$\Rightarrow\frac{1\times2\times\text{x}}{2}=\frac{3\times2\times\text{x}}{\text{x}}$
$\Rightarrow\text{x}=6$
Hence, $x = 6$

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Question 41 Mark

Which of the following statements are true? $40 : 200 = 1 : 5$

Answer

$40 : 200 = 1 : 5$
$\frac{40\ \text{men}}{200\ \text{men}}=\frac{1}{5}\ \text{or}\ \frac{40\ \text{men}\div40}{200\ \text{men}\div40}=\frac{\text{Rs. 5}\div5}{\text{Rs. 25}\div5}$
$\frac{1}{5}=\frac{1}{5}$ True.

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Question 51 Mark

Fill in the blanks: Ratio of $Rs. 2$ and $50$ paise and $Rs. 3$ and $75$ paise is .......

Answer

Ratio of $Rs. 2$ and $50$ paise and $Rs. 3$ and $75$ paise is $2 : 3. Rs. 2$ and $50$ paise $= (2 \times 100 + 50)$ paise $= 250$ paise $Rs. 3$ and $75$ paise $= (3 \times 100 + 75)$ paise $= 375$ paise
Now, $\frac{250}{375}=\frac{250\div25}{375\div25}$
$=\frac{10}{15}$
$=\frac{10\div5}{15\div5}$
$=\frac{2}{3}$ Hence, Ratio of $Rs. 2$ and $50$ paise and $Rs. 3$ and $75$ paise is $2 : 3$

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Question 61 Mark

Express the following in the language of ratios: In a class, the number of girls in the merit list of the board examination is two times that of boys.

Answer

Ratio of number of girls of girls to that of boys in the merit list is $2 : 1.$

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Question 71 Mark

Express the following ratios in language of daily life: In India, the ratio of the number of villages to that of cities is about $2000 : 1.$

Answer

The number of villages is $2000$ times that of cities in India.

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Question 81 Mark

Which of the following statements are true? $16 : 24 = 20 : 30$

Answer

$16 : 24 = 20 : 30$
$\Rightarrow\frac{16}{24}=\frac{20}{30}$
$\Rightarrow\frac{\frac{16}{24}}{\frac{4}{4}}=\frac{\frac{20}{30}}{\frac{5}{5}}$
$\Rightarrow\frac{4}{6}=\frac{4}{6}$
$\Rightarrow\frac{2}{3}=\frac{2}{3}$ True.

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Question 91 Mark

Fill in the blanks: Mean proportion of $2$ and $8$ is ......

Answer

Mean proportion of $2$ and $8$ is $4$.
Let the mean proportion of $2$ and $8$ be $x.$
Then, $2 : x : : x : 8$
$\Rightarrow\frac{2}{\text{x}}=\frac{\text{x}}{8}$
$\Rightarrow2\times8=\text{x}\times\text{x}$
$\Rightarrow16=\text{x}\times\text{x}$
$\Rightarrow4\times4=\text{x}\times\text{x}$
$\Rightarrow4=\text{x}$ Hence, mean proportion of $2$ and $8$ is $4$

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Question 101 Mark

Which of the following statements are true? $99 : 45 = 44 : 20$

Answer

$99 : 45 = 44 : 20$
$\frac{99\text{kg}}{45\text{kg}}=\frac{\text{Rs. 44}}{\text{Rs. 20}}$
$\Rightarrow\frac{99}{45}=\frac{44}{20}$
$\Rightarrow\frac{99\div9}{45\div9}=\frac{44\div9}{20\div9}$
$\Rightarrow\frac{11}{5}=\frac{11}{5}$ True.

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Question 111 Mark

Fill in the blanks: If $a : b = 4 : 5$ and $b : c = 2 : 3$, then $a : c =$ ......

Answer

If $a : b = 4 : 5$ and $b : c = 2 : 3,$
then $a : c = 8 : 15.$
It is given that, $\frac{\text{a}}{\text{b}}=\frac{4}{5}\ ....(1)$ and $\frac{\text{b}}{\text{c}}=\frac{2}{3}\ ....(2)$
Now, $\frac{\text{a}}{\text{c}}=\frac{\text{a}\div\text{b}}{\text{c}\div\text{b}}$
$=\frac{\text{a}}{\text{b}}\times\frac{\text{b}}{\text{c}}$
$=\frac{4}{5}\times\frac{2}{3}\ [\text{From (1) and (2)}]$
$=\frac{8}{15}$
Hence, $a : c = 8 : 15$

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Question 121 Mark

Which of the following statements are true?
$51 : 58 = 85 : 102$

Answer

$51 : 58 = 85 : 102$
$\frac{51}{58}\neq\frac{5}{6}$
False.

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Question 131 Mark

Express the following in the language of ratios: The number of student passing mathematics test is $\frac{2}{3}$ of the number that appeared.

Answer

Ratio of number of students passing a mathematics test to that of total students appearins in test is $2 : 3.$

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Question 141 Mark

Fill in the following blanks: $\frac{12}{20}=\frac{\Box}{5}=\frac{9}{\Box}$

Answer

$\frac{12}{20}=\frac{3}{5}$ (Dividing numerator and denminator by 4) $\frac{3}{5}=\frac{9}{15}$ (Multiplying numerator and denominator by 3) $\therefore\frac{12}{20}=\frac{3}{5}=\frac{9}{15}$

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Question 151 Mark

Which of the following statements are true? $21 : 6 = 35 : 10$

Answer

$21 : 6 = 35 : 10$
$\Rightarrow\frac{\frac{21}{6}}{\frac{3}{3}}=\frac{\frac{35}{10}}{\frac{5}{5}}$
$\Rightarrow\frac{7}{2}=\frac{7}{2}$ True.

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Question 161 Mark

Fill in the blanks: If $2x = 5y$, then $x : y =$ ......

Answer

If $2x = 5y$, then $x : y = 5 : 2.$
It is given that, $2x = 5y ...... (1)$
Now, $2x = 5y$
$\Rightarrow\frac{2\text{x}}{2\text{y}}=\frac{5\text{y}}{2\text{y}}$
$\Rightarrow\frac{\text{x}}{\text{y}}=\frac{5}{2}$
Hence, $x : y = 5 : 2.$

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MCQ 171 Mark

Two numbers are in the ratio $7 : 9.$ If the sum of the numbers is $112,$ then the larger number is:

✓
$63$
B
$42$
C
$49$
D
$72$

Answer

Correct option: A.

$63$

Then $= 7x + 9x = 112$
$= 16x = 112$
$= x = 7$
Now, Let the larger number be $= 9 \times 7 = 63$

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