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39 questions · timed · auto-graded

Question 21 Mark
$3 : 33 = 33 : 333$
Answer
Given, $3 : 33 = 33 : 333$
$\frac{3}{33}=\frac{33}{333}$
Simplest form of $\frac{3}{33}=\frac{1}{11}$ [On dividing numerator and denominator by $3]$
Simplest form of $\frac{33}{333}=\frac{11}{111}$ [On dividing numerator and denominator by $3]$
$\frac{1}{11}\ne\frac{11}{111}$
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Question 31 Mark
A ratio can be equal to $1.$
Answer
A ratio can be equal to $1$, if both quantities are same.
e.g. ratio of $50g$ to $50g$ is = $\frac{50}{50}=1$
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Question 41 Mark
The ratio of $1$ hour to one day is $1 : 1.$
Answer
Ratio of 1h to one day = $\frac{1\text{h}}{1\text{day}}=\frac{1\text{h}}{24\text{h}}$
$[\because1\text{day}=24\text{h}]$
$=\frac{1}{24}$
$=1:24$
$=1:24\ne1:1$
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Question 51 Mark
$15m : 40m = 35m : 65m$
Answer
 Given, $15m : 40m = 35m : 65m$
$\frac{15}{40} =\frac{35}{65}$
Simplest form of $\frac{15}{40} =\frac{3}{8}$ [On dividing numerator and denominator by $5]$
Simplest form of $\frac{35}{65} =\frac{7}{13}$ [On dividing numerator and denominator by $5]$
$\frac{3}{8}\ne\frac{7}{13}$
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Question 61 Mark
$5\ kg : 7.5\ kg = Rs. 7.50 : Rs. 5$
Answer
Given, $5\ kg : 7.5\ kg = Rs. 7.50 : Rs. 5$
$\Rightarrow\frac{5}{7.5} =\frac{7.50}{5}$
Simplest form of $\frac{5}{7.5} =\frac{1}{1.5}$ [On dividing numerator and denominator by $5]$
Simplest form of $\frac{7.50}{5} =\frac{1.5}{1}$ [On dividing numerator and denominator by $5]$
$\frac{1}{1.5}\ne\frac{1.5}{1}$
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Question 71 Mark
To find the ratio of two quantities, they must be expressed in units.
Answer
Solution:
To find the ratio of two quantities, they must be expressed in same units.
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Question 81 Mark
$\frac{3}{5}=\frac{\Box}{20}$
Answer
We have, $\frac{3}{5}=\frac{?}{20}$
$\Rightarrow\frac{3\times4}{5\times4}=\frac{?}{20}$
$\Rightarrow\frac{12}{20}=\frac{?}{20}$ On comparing, we get $?=12$
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Question 91 Mark
$\frac{3}{8}=\frac{15}{40}$
Answer
True. Solution: Given, $\frac{3}{8}=\frac{15}{40}$
Simplest form of $\frac{15}{40}=\frac{3}{8}$ [On dividing numerator and denominator by $5]$
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Question 101 Mark
$4 : 7 = 20 : 35$
Answer
Given, $4 : 7 = 20 : 35$
Simplest form of $\frac{20}{35}=\frac{4}{7}$ [On dividing numerator and denominator by $5]$
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Question 111 Mark
There is a number in the box $\Box$ such that $\Box$, $24, 9, 12$ are in proportion. The number in the box is .
Answer
Let the number in box is $x$, then $x, 24, 9$ and $12$ are in proportion.
$\therefore x:24::9:12$
$\Rightarrow\frac{\text{x}}{24}=\frac{9}{12}$
$\Big[\because\text{If a, b, c and d are in proportion, then}\frac{\text{a}}{\text{b}}=\frac{\text{c}}{\text{d}}\Big]$
$\Rightarrow\text{x}\times12=24\times9$
$\Rightarrow\text{x}=\frac{24\times9}{12}$
$\Rightarrow\text{x}=2\times9$
$\therefore\ \text{x}=18$ The number in the box is $18.$
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Question 121 Mark
$20m : 70m = Rs. 8 : Rs. .$
Answer
$\frac{20\text{m}}{70\text{m}}=\frac{\text{Rs.}\ 8}{\text{x(let)}}$
$\Rightarrow\frac{20}{70}=\frac{8}{\text{x}}$
$\Rightarrow20\times\text{x} = 70\times8$ [by cross multiplication]
$\Rightarrow\text{x}=\frac{70\times8}{20}=28$
$20m : 70m = Rs. 8 : Rs. 28$
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Question 131 Mark
$20g : 100g = 1$ metre $: 500\ cm$
Answer
Given, $20g : 100g = 1$ metre $: 500\ cm$
$\frac{20}{100} =\frac{100}{500}$
Simplest form of $\frac{20}{100} =\frac{1}{5}$
Simplest form of $\frac{100}{500} =\frac{1}{5}$
$\frac{1}{5}=\frac{1}{5}$
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Question 141 Mark
Sleeping time of a python in a $24$ hour clock is represented by the shaded portion in Fig. The ratio of sleeping time to awaking time is .
Answer
 By observing above figure, we have sleeping time of python $=18h$
Awaking time of python $= (24 - 18) = 6h$
Ratio of sleeping time to awaking time = $\frac{18\text{h}}{6\text{h}}$
$=\frac{3}{1}$ [On dividing numerator and denominator by $6] = 3 : 1$
The number in the box is $18.$
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Question 151 Mark
$\frac{\Box}{45}=\frac{16}{40}=\frac{24}{\Box}$
Answer
We have, $\frac{?}{45}=\frac{16}{40}=\frac{24}{?}$
For first $2$ ratios, $\frac{16}{40}=\frac{2\times8}{5\times8}=\frac{2\times9}{5\times9}=\frac{18}{45}$
Hence, missing number $= 18$ For last $2$ ratios, $\frac{16}{40}=\frac{2\times8}{5\times8}=\frac{2\times12}{5\times12}=\frac{24}{60}$
Hence, missing number $= 18$
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Question 161 Mark
$\frac{\Box}{18}=\frac{2}{9}$
Answer
We have, $\frac{?}{18}=\frac{2}{9}$
$\Rightarrow\frac{?}{18}=\frac{2\times2}{9\times2}$
$\Rightarrow\frac{?}{18}=\frac{4}{18}$ On comparing, we get $?=4$
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Question 171 Mark
The ratio of $10\ kg$ to $100\ kg$ is $1 : 10$
Answer
Ratio of $10\ kg$ to $100\ kg =\frac{10\text{kg}}{100\text{kg}}$
$\frac{1}{10}$ [On dividing numerator and denominator by $10]$
$1 : 10$
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Question 181 Mark
The ratio of $150\ cm$ to $1$ metre is $1 : 1.5.$
Answer
Ratio of $150\ cm$ to $1$ metre $=\frac{150\text{cm}}{1\ \text{metre}}=\frac{150\text{cm}}{100\text{cm}}$
$[ \because1\text{m}=100\text{cm}]$
$\frac{3}{2}$ [On dividing numerator and denominator by $50]$
$3 : 2$
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Question 191 Mark
The ratio $4 : 16$ is in its lowest form.
Answer
Ratio of $4 : 16$ in lowest form is
$=\frac{4}{16}$
$=\frac{1}{4}$
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Question 201 Mark
$27\ cm^2: 57\ cm^2= 18\ cm : 38\ cm$
Answer
Given, $27\ cm^2: 57\ cm^2= 18\ cm : 38\ cm$
$\frac{27}{57} =\frac{18}{38}$
Simplest form of $\frac{27}{57} =\frac{9}{19}$ [On dividing numerator and denominator by $3]$
Simplest form of $\frac{18}{38} =\frac{9}{19}$ [On dividing numerator and denominator by $2]$
$\frac{9}{19}=\frac{9}{19}$
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Question 211 Mark
If two ratios are equal, then they are in . Use Fig. (In which each square is of unit length) for question:
Answer
If two ratios are equal, then they are in proportion. Solution: Use following figure (in which each square is unit of length) for question:
 
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Question 221 Mark
Which pair of ratios are equal? And why?$\frac{4}{5},\frac{12}{20}$
Answer
Given, $\frac{4}{5},\frac{12}{20}$
Simplest form of $\frac{12}{20}=\frac{3}{5}$
$\frac{4}{5}\ne\frac{3}{5}$
Hence, $\frac{4}{5},\frac{12}{20}$ ratios are not equal.
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Question 231 Mark
Saturn and Jupiter take $9$ hours $56$ minutes and $10$ hours $40$ minutes, respectively for one spin on their axes. The ratio of the time taken by Saturn and Jupiter in lowest form is .
Answer
Saturn takes time for one spin $= 9h 56$min $= (9 × 60 + 56)min$ [ $1h = 60min$] $= 596min$
Jupiter takes time for one spin $= 10h 40min = (10 × 60 + 40)min = 640min$
Ratio of time taken by Saturn to Jupiter $\frac{596}{640} =\frac{149}{160}$ $= 149 : 160$
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Question 241 Mark
$25\ kg : 20g = 50\ kg : 40g$
Answer
Given, $25\ kg : 20g = 50\ kg : 40g$
$\Rightarrow\frac{25\text{kg}}{20\text{g}}=\frac{50\text{kg}}{40\text{g}}$
$\Rightarrow\frac{25000\text{g}}{20\text{g}}=\frac{50000\text{g}}{40\text{g}}$
$[ \because1\text{kg}=1000\text{g}]$
Simplest form of $\frac{25000}{20}=\frac{1250}{1}$ [On dividing numerator and denominator by $20]$
Simplest form of $\frac{50000}{40}=\frac{1250}{1}$ [On dividing numerator and denominator by $20]$
$1250 = 1250$
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Question 251 Mark
$\frac{8}{\Box}=\frac{3.2}{4}$
Answer
We have, $\frac{8}{?}=\frac{3.2}{4}$
$\Rightarrow\frac{8}{?}=\frac{3.2\times2.5}{4\times2.5}$
$\Rightarrow\frac{8}{?}=\frac{8}{10}$ On comparing, we get $?=10$
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Question 261 Mark
$0.2 : 5 = 2 : 0.5$
Answer
False.Solution:
Given, $0.2 : 5 = 2 : 0.5$
$\frac{0.2}{5}=\frac{2}{0.5}$
$\Rightarrow\frac{2}{50}\ne\frac{20}{5}$
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Question 271 Mark
$\frac{16}{36}=\frac{\Box}{63}=\frac{36}{\Box}=\frac{\Box}{117}$
Answer
We have, $\frac{16}{36}=\frac{?}{63}=\frac{36}{?}=\frac{?}{117}$
For first $2$ ratios, $\frac{16}{36}=\frac{4\times4}{9\times4}=\frac{4\times7}{9\times7}=\frac{28}{63}$
Hence, missing number $= 28$ For middle $2$ ratios,
$\frac{28}{63}=\frac{36}{?}$
$\frac{28}{63}=\frac{4\times7}{9\times7}=\frac{4\times9}{9\times9}=\frac{36}{81}$
Hence, missing number = 81 For last 2 ratios, $\frac{36}{81}=\frac{?}{117}$
$\frac{36}{81}=\frac{4\times9}{9\times9}=\frac{4\times13}{9\times13}=\frac{52}{117}$
Hence, missing number $= 52$
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Question 281 Mark
A ratio expressed in lowest form has no common factor other than in its terms.
Answer
Solution: A ratio expressed in lowest form has no common factor other than one(1) in its terms.
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Question 291 Mark
$12$ hours : $30$ hours $= 8\ km : 20\ km$
Answer
Given, $12$ hours : $30$ hours $= 8\ km : 20\ km$
$\frac{12}{30} =\frac{8}{20}$
Simplest form of $\frac{12}{30} =\frac{2}{5}$ [On dividing numerator and denominator by $6]$
Simplest form of $\frac{8}{20} =\frac{2}{5}$ [On dividing numerator and denominator by $4]$
$\frac{2}{5}=\frac{2}{5}$
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Question 301 Mark
Ratio of $5$ paise to $25$ paise is the same as the ratio of $20$ paise to .
Answer
Ratio of $5$ paise to $25$ paise is the same as the ratio of $20$ paise to $x$ (let).
$\frac{5\ \text{paise}}{25\ \text{paise}}=\frac{20\ \text{paise}}{\text{x}\ \text{paise}}$
$\Rightarrow\frac{5}{25}=\frac{20}{\text{x}}$
$\Rightarrow5\times\text{x}=25\times20$
$\Rightarrow\text{x}=\frac{25\times20}{5}$
$\Rightarrow\text{x}=100 = 100$ paise or $Rs. 1$
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Question 311 Mark
The ratio of the perimeter of the boundary of the shaded portion to the perimeter of the whole figure is .
Answer
 
The perimeter of whole figure $= 14$ units
The perimeter of shade figure $= 6$ units
Ratio of perimeter of shaded portion to whole figure = $\frac{6\ \text{units}}{14\ \text{units}}$
$=\frac{3}{7}$ [On dividing numerator and denominator by $2]$
$= 3 : 7$
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Question 321 Mark
The ratio $5 : 4$ is different from the ratio $4 : 5.$
Answer
Ratio of $5 : 4 = \frac{5}{4} = 1.25$
$\Rightarrow $ Ratio of $4 : 5 = \frac{4}{5 }= 0.80$
Hence, the ratio of $5 : 4$ is different from the ratio $4 : 5.$
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Question 331 Mark
The ratio of the area of the shaded portion to that of the whole figure is .
Answer
Area of shaded portion = Length $\times $ Breadth $= 2 \times 1 = 2$ sq units
Area of shaded figure = Length $\times $ Breadth $= 4 \times 3 = 12$ sq units
Ratio of shaded portion to whole figure =$\frac{2}{12}$
$=\frac{1}{6} = 1 : 6$
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Question 341 Mark
A ratio will always be more than $1.$
Answer
A ratio can be equal to $1$, more than $1$ and less than $1.$
e.g. $\frac{3}{2} = 1.5(> 1)$, $\frac{2}{2} = 1 (= 1)$and $\frac{3}{4} = 0.75(< 1)$
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Question 351 Mark
If $b : a = c : d$, then $a, b, c, d$ are in proportion.
Answer
If $b : a = c : d$
$\Rightarrow \frac{\text{b}}{\text{a}}=\frac{\text{c}}{\text{d}}$
If a, to, c and d are in proportion, then
$\frac{\text{a}}{\text{b}}=\frac{\text{c}}{\text{d}}$
$= ad : bc$
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Question 361 Mark
Which pair of ratios are equal? And why?$\frac{2}{3},\frac{4}{6}$
Answer
Given, $\frac{2}{3},\frac{4}{6}$
Simplest form of $\frac{4}{6}=\frac{2}{3}$
$\frac{2}{3}=\frac{2}{3}$
Hence, $\frac{2}{3},\frac{4}{6}$ ratios are equal.
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Question 371 Mark
Which pair of ratios are equal? And why?$\frac{8}{4},\frac{2}{1}$
Answer
Given, $\frac{8}{4},\frac{2}{1}$ Simplest form of $\frac{8}{4}=\frac{2}{1}$ $\frac{2}{1}=\frac{2}{1}$ Hence, $\frac{8}{4},\frac{2}{1}$ ratios are equal.
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Question 381 Mark
$10g$ of caustic soda dissolved in $100mL$ of water makes a solution of caustic soda. Amount of caustic soda needed for $1$ litre of water to make the same type of solution is .
Answer
Given, $10g$ of caustic soda dissolved in $100ml$ water.
The ratio of caustic soda to water should be in proportion. $10g : 100ml :: x g : 1L$ 
$\frac{10\text{g}}{100\text{ml}}=\frac{\text{x g}}{1000\text{ml}} [1L = 1000ml]$
$\Rightarrow\text{x g}\times100\text{ml}=10\text{g}=\times1000\text{ml}$ [By cross multiplication]
$\Rightarrow\text{x g}=\frac{10\text{g}\times1000\text{ml}}{100\text{ml}} x = 100g$
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Question 391 Mark
The two terms of a ratio can be in two different units.
Answer
False.Solution:
For a ratio, the two quantities must be in the same unit.
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