[1 Mark Question Answer]

Question 11 Mark

Find the mean proportional between 3 and 27

Answer

Mean proportional between 3 and 27
$\sqrt{3 \times 27}=\sqrt{81}=9$

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Question 21 Mark

Find the mean proportional between 16 and 4

Answer

Mean proportional between 16 and 4
$\sqrt{16 \times 4}=\sqrt{64}=8$

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Question 31 Mark

Find the third proportional of $\frac{1}{7}$ and $\frac{3}{14}$

Answer

Third proportional to $\frac{1}{7}$ and $\frac{3}{14}$
$=\frac{\frac{3}{14} \times \frac{3}{14}}{\frac{1}{7}}=\frac{9}{196} \times \frac{7}{1}=\frac{9}{28}$

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Question 41 Mark

Find the third proportional of 2 m 40 cm and 40 cm

Answer

Third proportional to $2 \mathrm{~m} 40 \mathrm{~cm}$ and $40 \mathrm{~cm}$ or $240 \mathrm{~cm}$ and $40 \mathrm{~cm}$
$\frac{40 \times 40}{240}=\frac{20}{3}=6 \frac{2}{3} \mathrm{~cm}$

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Question 51 Mark

Find the third proportional of 27 and 9

Answer

Third proportional of 27 and 9
$=\frac{9 \times 9}{27}=3$

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Question 61 Mark

Find the fourth proportional of 2.1, 1.5 and 8.4

Answer

Fourth proportional of 2.1, 1.5 and 8.4
$=\frac{1.5 \times 8.5}{2.1}=1.5 \times 4=6.0$

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Question 71 Mark

Find the fourth proportional of 5, 9 and 45

Answer

Fourth proportional of 5,9 and 45
$=\frac{9 \times 45}{5}=81$

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Question 81 Mark

Find the fourth proportional of 3, 12 and 4

Answer

Fourth proportional of 3, 12 and 4
$=\frac{12 \times 4}{3}=16$

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Question 91 Mark

Express the given ratio in its simplest form: 3 hours : 1 day

Answer

3 hours : 1 day $=3$ hours : 24 hours $\ldots(1$ day $=24$ hours $)$
$=\frac{3}{24}=\frac{1}{8}=1: 8$

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Question 101 Mark

Express the given ratio in its simplest form: 200 m : 5 km

Answer

$\begin{aligned} & 200 \mathrm{~m}: 5 \mathrm{~km}=200 \mathrm{~m}: 5000 \mathrm{~m} \ldots .(1 \mathrm{~km}=1000 \mathrm{~m}) \\ & =\frac{200}{5000}=\frac{200 \div 200}{5000 \div 200} \ldots(\mathrm{HCF} \text { of } 200,5000=200) \\ & =\frac{1}{25}=1: 25\end{aligned}$

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Question 111 Mark

Express the given ratio in its simplest form: 10 paise : ₹ 1

Answer

10 paise : ₹ 1 = 10 paise : 100 paise ...( 1 Rs. $=100$ paise $)$
$=\frac{10}{100}=\frac{1}{10}=1: 10$

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Question 121 Mark

Express the given ratio in its simplest form: 40 kg : 1 quintal

Answer

$\begin{aligned} & 40 \mathrm{~kg}: 1 \text { quintal }=40 \mathrm{~kg}: 100 \mathrm{~kg} \ldots(1 \text { quintal }=100 \mathrm{~kg}) \\ & =\frac{40}{100}=\frac{40 \div 20}{100 \div 20}=\frac{2}{5} \\ & \quad(\mathrm{HCF} \text { of } 40,100=20) \\ & =2: 5\end{aligned}$

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Question 131 Mark

Express the given ratio in its simplest form: $6 \frac{1}{4}: 12 \frac{1}{2}$

Answer

$\begin{aligned} & 6 \frac{1}{4}: 12 \frac{1}{2}=\frac{25}{4}: \frac{25}{2} \\ & =\frac{25}{4} \times \frac{2}{25} \\ & =\frac{2}{4}=\frac{1}{2}=1: 2\end{aligned}$

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Question 141 Mark

Express the given ratio in its simplest form: 1.5 : 2.5

Answer

$\begin{aligned} & 1.5: 2.5=\frac{1.5}{2.5}=\frac{15}{25} \\ & =\frac{15 \div 5}{25 \div 5}=\frac{3}{5}(\text { HCF of } 15,25=5) \\ & =3: 5\end{aligned}$

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Question 151 Mark

Express the given ratio in its simplest form: 22 : 66

Answer

$\begin{aligned} & 22: 66=\frac{22}{66} \\ & =\frac{22 \div 22}{66 \div 22}=\frac{1}{3}(\mathrm{HCF} \text { of } 22 \text { and } 66=22) \\ & =1: 3\end{aligned}$

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