[2 Mark Question Answer]

Question 12 Marks

Find the mean proportional between $\frac{1}{4}$ and $\frac{1}{16}$

Answer

Mean proportional between $\frac{1}{4}$ and $\frac{1}{16}$
$ \begin{aligned} & =\sqrt{\frac{1}{4} \times \frac{1}{16}} \\ & =\sqrt{\frac{1}{64}}=\frac{1}{8} \end{aligned} $

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Question 22 Marks

Find the mean proportional between 0.9 and 2.5

Answer

Mean proportional between 0.9 and 2.5
$ \begin{aligned} & =\sqrt{0.9 \times 2.5} \\ & =\sqrt{\frac{9}{10} \times \frac{25}{10}} \\ & =\sqrt{\frac{225}{100}}=\frac{15}{10} \\ & =1.5 \end{aligned} $

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Question 32 Marks

Find the third proportional of 1.6 and 0.8

Answer

Third proportional to 1.6 and 0.8
$ \begin{aligned} & =\frac{0.8 \times 0.8}{1.6}=\frac{0.64}{1.6} \\ & =\frac{64}{160}=\frac{2}{5}=0.4 \end{aligned} $

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Question 42 Marks

Find the third proportional of 1.8 and 0.6

Answer

Third proportional to 1.8 and 0.6
$ \begin{aligned} & =\frac{0.6 \times 0.6}{1.8}=\frac{0.36}{1.8}=\frac{36}{180} \\ & =\frac{1}{5}=0.2 \end{aligned} $

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Question 52 Marks

Find the fourth proportional of $\frac{1}{3}, \frac{2}{5}$ and 8.4

Answer

Fourth proportional of $\frac{1}{3}, \frac{2}{5}$ and 8.4
$ \begin{aligned} & =\frac{\frac{2}{5} \times 8.4}{\frac{1}{3}}=\frac{2}{5} \times 8.4 \times \frac{3}{1} \\ & =\frac{2 \times 84 \times 3}{5 \times 10 \times 1}=\frac{252}{25}=10.08 \end{aligned} $

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Question 62 Marks

The ratio between two quantities is 3: the first is Rs. 810, find the second.

Answer

Ratio between two quantities $=3: 4$
$ \begin{aligned} & \text { Sum of ratio }=3+4=7 \\ & \therefore \text { Second quantity }=\text { Rs. } \frac{810 \times 4}{3} \\ & =\text { Rs. } 270 \times 4=\text { Rs. } 1080 \end{aligned} $

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Question 72 Marks

Rs. 720 is divided between x and y in the ratio 4:5. How many rupees will each get?

Answer

Total amount $=$ Rs. 720 Ratio between $x, y=4: 5$
Sum of ratios $=4+5=9$
$ \begin{aligned} & x^{\prime} \text { s share }=\frac{4}{9} \text { of Rs. } 720=\text { Rs. } 320 \\ & \text { y's share }=\frac{5}{9} \text { of Rs. } 720=\text { Rs. } 400 \end{aligned} $

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Question 82 Marks

The ratio between two numbers is 5 : 9. Find the numbers, if their H.C.F. is 16.

Answer

Let the first number be 5x and second number be 9x
H.C.F. of 5x and 9x = Largest number common to 5x and 9x = x
Given H.C.F. = 16 ⇒ x = 16
∴ Required numbers = 5x and 9x = 5×16 and 9×16 = 80 and 144

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Question 92 Marks

Divide 64 cm long string into two parts in the ratio 5 : 3.

Answer

Sum of ratios $=5+3=8$
$\therefore$ first part $=\frac{5}{8}$ of $64 \mathrm{~cm}=40 \mathrm{~cm}$
Second part $=\frac{3}{8}$ of $64 \mathrm{~cm}=24 \mathrm{~cm}$

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Question 102 Marks

Express the given ratio in its simplest form: $1 \frac{1}{3}: 2 \frac{1}{4}: 2 \frac{1}{2}$

Answer

$\begin{aligned} & 1 \frac{1}{3}: 2 \frac{1}{4}: 2 \frac{1}{2}=\frac{4}{3}: \frac{9}{4}: \frac{5}{2} \\ & =\frac{16: 27: 30}{12} \ldots(\text { LCM of } 3,4,2=12) \\ & =16: 27: 30\end{aligned}$

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Question 112 Marks

Express the given ratio in its simplest form: 6 months: $1 \frac{1}{3}$ years

Answer

6 months: $1 \frac{1}{3}$ years $=6$ months $: \frac{4}{3} \times 12$ months
$=6$ months $: 16$ months
$=\frac{6}{16}=\frac{6 \div 2}{16 \div 2}=\frac{3}{8}=3: 8$

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Question 122 Marks

Two poles of different heights are standing vertically on a horizontal field. At a particular time, the ratio between the lengths of their shadows is 2 :3. If the height of the smaller pole is 7.5 m, find the height of the other pole.

Answer

Ratio between the shadows of two poles $=2: 3$
$\therefore$ Height of smaller pole $=7.5 \mathrm{~m}$
Height of taller pole $=\frac{7.5 \times 3}{2}$
$=\frac{22.5}{2}=11.25$

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Question 132 Marks

In a class, the ratio of boys to the girls is 7:8. What part of the whole class are girls?

Answer

Ratio between boys and girls $=7: 8$
Sum of ratios $=7+8=15$
$\therefore$ Girls are $\frac{8}{15}$ of the whole class.

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