Question 12 Marks
Express the following ratios in its simplest form: $186 : 403$
AnswerThe given ratio is $186 : 403$
$=\frac{186}{402}$ To express this ratio in the simplest form,
we will have to find the $H.C.F$ of $186$ and $403,$ It is $31.$
Dividing each term of the ratio by the $H.C.F$ of its terms i.e. $31,$ we get $186 : 403$ is $6 : 23.$
View full question & answer→Question 22 Marks
Find the ratio of: $25$ paise to $Rs. 60.$
Answer$25$ paise to $Rs. 60 = 25$ paise : $Rs. 60 = 25$ paise : $6000$ paise $= 1 : 240 [ \because H.C.F = 25$ paise$]$
View full question & answer→Question 32 Marks
Express the following ratios in its simplest form: $85 : 391$
AnswerTo express this ratio in the simplest form we will have to find the $H.C.F$ of $85$ and $391,$
It is $17.$ Dividing each term of the ratio by the $H.C.F$ of its terms i.e. $17,$
we get $\frac{85}{391}=\frac{85\div17}{391\div17}=\frac{\frac{85}{17}}{\frac{391}{17}}=\frac{5}{23}$
Hence, the simplest form of the ratio $85 : 391$ is $5 : 23.$
View full question & answer→Question 42 Marks
$2$ dozens of oranges cost $Rs. 60.$ Find the cost of $120$ similar oranges$?$
AnswerCost of $2$ dozens or $24$ oranges $= Rs. 60$
Cost of $1$ orange $= Rs. 6024$
Cost of $120$ oranges $= 6024 \times 120 = Rs. 300$
View full question & answer→Question 52 Marks
If $4, x, 9$ are in continued proportion, find the value $x.$
Answer$\Rightarrow\frac{4}{\text{x}}=\frac{\text{x}}{9}$
By cross multiplication we get,
$\Rightarrow4{9}=\text{x}^2$
$\Rightarrow\text{x}^2=36$
$\Rightarrow\text{x}=6$
View full question & answer→Question 62 Marks
Find $x$ in the following proportions: $x : 6 = 55 : 11$
Answer$x : 6 = 55 : 11$
$\Rightarrow\frac{\text{x}}{6}=\frac{55}{11}$
By cross multiplication we get,
$\Rightarrow\ 11\text{x}=6\times55$
$\Rightarrow\ 11\text{x}=330$
$\Rightarrow\ \text{x}=\frac{330}{11}$
$\Rightarrow\ \text{x}=30$
View full question & answer→Question 72 Marks
Find the ratio of: $10$ metres to $25\ cm.$
Answer$10$ metres to $25\ cm = 10$ metres $: 25\ cm= 1000\ cm : 25\ cm$
$= 40 : 1$
$[H.C.F = 25]$
View full question & answer→Question 82 Marks
Which ratio is larger in the following pairs$?\ 1 : 2$ or $13 : 27$
Answer$1:2=\frac{1}{2}\ \text{and}\ 13:27=\frac{13}{27}$
Now, $LCM$ of $2$ and $27$ is $54$
$\frac{27}{54}\ \text{or}\ \frac{26}{54}$
$\therefore\frac{1}{2}>\frac{13}{27}$
View full question & answer→Question 92 Marks
Find $x$ in the following proportions: $18 : x = 27 : 3$
Answer$18 : x = 27 : 3$
$\Rightarrow\frac{18}{\text{x}}=\frac{27}{3}$
$\Rightarrow\ 18\times3=\text{x}(27)$
$\Rightarrow\ 27\text{x}=54$
$\Rightarrow\ \text{x}=\frac{54}{27}$
$\Rightarrow\ \text{x}=2$
View full question & answer→Question 102 Marks
Find $x$ in the following proportions: $16 : 18 = x : 96$
Answer$16 : 18 = x : 96$
$\Rightarrow\frac{16}{18}=\frac{\text{x}}{96}$
$\Rightarrow\frac{8}{9}=\frac{\text{x}}{96}$
By cross multiplication we get,
$\Rightarrow8(96)=9\text{x}$
$\Rightarrow\frac{778}{9}=\text{x}$
$\Rightarrow\text{x}=\frac{256}{3}$
View full question & answer→Question 112 Marks
A car travels $165\ km$ in $3$ hours.
How long will it take to travel $440\ km?$
AnswerA car travels $165\ km$ in $3$ hours,
Speed of the car $=$ Distance Time $= 1653 = 55\ km/ h$
Time taken by the car to travel $440\ km = 44055 = 8$ hours.
View full question & answer→Question 122 Marks
Find which of the following are in proportion:
$150, 250, 200, 300$
AnswerWe have,
$\frac{150}{250}=\frac{3}{5}\ \text{and}\ \frac{200}{300}=\frac{4}{6}=\frac{2}{3}$
$\therefore$ Hence, $150, 250 200, 300$ are not in proportion.
View full question & answer→Question 132 Marks
Find which of the following are in proportion: $8, 16, 6, 12$
AnswerWe have,$\text{and}\ \frac{6}{12}=\frac{1}{2}$
$\therefore\frac{8}{16}=\frac{6}{12}$
Hence $8, 16, 6, 12$ are in proportion.
View full question & answer→Question 142 Marks
Find the ratio of: $10$ litres to $0.25$ litre.
Answer$10$ litres to $0.25$ litres $= 10 : 0.25 = 40 : 1 [\because H.C.F = 0.25]$
View full question & answer→Question 152 Marks
Find the ratio of the following in the simplest form: $2$ metres to $35\ cm.$
Answer$2$ meters to $35\ cm = 2$ met $: 35\ cm = 200\ cm : 35\ cm [1m = 100\ cm] = 40 : 7 [ \because$ dividing the first and second term by their $H.C.F = 5].$
View full question & answer→Question 162 Marks
Find which of the following are in proportion:
$6, 2, 4, 3$
AnswerWe have,$\frac{6}{2}=\frac{3}{1}\ \text{and}\ \frac{4}{3}=\frac{4}{3}$
$\therefore\frac{3}{1}\neq\frac{4}{3}$
Hence, $6, 2, 4, 3$ are not in proportion.
View full question & answer→Question 172 Marks
The weight of $45$ folding chairs is $18\ kg.$ How many such chairs can be loaded on a truck having a capacity of carrying $4000\ kg$ load$?$
AnswerNumber of folding chairs weighing $18\ kg = 45$ Number of folding chairs weighing$ 1\ kg = 4518$ Number of folding chairs weighing $4,000\ kg = 4518 \times 4000 = 10000$
View full question & answer→Question 182 Marks
Show that the following numbers are in continued proportion: $48, 60, 75$
Answer$48, 60, 75$
$\frac{48}{60}=\frac{60}{75}$
$\Rightarrow\frac{4}{5}=\frac{4}{5}$
$\therefore 48, 60, 75$ are in continued proportion.
View full question & answer→Question 192 Marks
Find the ratio of the following in the simplest form: $48 \min$ to $2$ hours $40 \min.$
Answer$48 \min$ to $2$ hours $40 \min = 48 \min : 160 \min [ \because 1$ hour $= 60 \min]$
$= 3 : 10 [ \because$ dividing the first and second term by their $H.C.F = 3 : 10].$
View full question & answer→Question 202 Marks
Find the ratio of the following in the simplest form: $75$ paisa to $Rs. 3.$
Answer$75$ paise to $Rs.3 = 75$ paise $: Rs. 3 = 75$ paise $: 300$ paise $= 1 : 4 [\because\ \text{IRS}=100\ \text{paise}]$
$[$Dividing the first and second term by their $H.C.F = 75].$
View full question & answer→Question 212 Marks
Find the ratio of the following in the simplest form: $35$ minutes to $45$ seconds.
Answer$35$ minutes to $45$ seconds $= 35 \min : 45 \sec = 2100 \sec : 45 \sec = 140 : 3 [H.C.F = 15].$
View full question & answer→Question 222 Marks
Find the ratio of the following in the simplest form: $8\ kg$ to $400\ gm.$
Answer$\text{8kg to 400gm = 8kg : 400gm = 8000gm : 400gm = 20 : 1.} $ $\text{ [Dividing the first and second terms by their H.C.F = 400].}$
View full question & answer→Question 232 Marks
Find the ratio of the following in the simplest form: $3\ m\ 5\ cm$ to $35\ cm.$
Answer$3m\ 5\ cm$ to $35\ cm = 3m\ 5\ cm : 35\ cm [ \because 1 $ hour $= 100 \min] = 305\ cm : 35\ cm [$Dividing the first and second terms by their $H.C.F = 5] = 61 : 7.$
View full question & answer→Question 242 Marks
A rail journey of $75\ km$ costs $Rs. 215.$ How much will a journey of $120\ km$ cost$?$
AnswerCost of a rail journey of $75\ km = Rs. 215$
Cost of a rail journey of $1\ km = Rs. 21575$
Cost of a rail journey of $120\ km = 21575 \times 120 = Rs. 344$
View full question & answer→Question 252 Marks
Find the ratio of the following in the simplest form:$48$ minutes to $1$ hour.
Answer$48$ minutes to $1$ hour $= 48 \min : 1$ hour $= 48 \min : 60 \min [ \because 1$ hour $= 60 \min] = 4 : 5.$
$[$Dividing the first and second term by their $H.C.F = 12].$
View full question & answer→Question 262 Marks
Express the following ratios in its simplest form: $60 : 72$
AnswerTo express this ratio in the simplest form, we will have to find the $H.C.F$ of $60$ and $72. $
It is $12$ dividing each term of the ration by the $H.C.F$ of its terms
i.e. $12$ we get $\frac{60}{12}=\frac{60\div12}{72\div12}=\frac{5}{6}\text{or}\ 5 : 6.$
Hence, the simplest form of the ratio $60 : 72$ is $5 : 6.$
View full question & answer→Question 272 Marks
The cost of $17$ chairs is $Rs. 19210.$ Find the number of such chairs that can be purchased in $Rs. 113000?$
AnswerNumber of chairs purchased in $Rs. 19,210 = 17$
Number of chairs purchased in $Rs. 1 = 1719210$
Number of chairs purchased in $Rs. 1,13,000 = 1719210 \times 113000 = 100$
View full question & answer→Question 282 Marks
Find the ratio of the following in the simplest form: $2$ dozen to $3$ scores.
Answer$2$ dozen to $3$ scores $= 2$ dozen$ : 3$ scores $= 24 : 60 [ \because 1$ dozen $= 12$ score$ = 20] = 2 : 5. [$Dividing the first and second term by their $H.C.F = 12].$
View full question & answer→Question 292 Marks
Express the following ratios in its simplest form: $324 : 144$
AnswerTo express this ratio in the simplest form,
we will have to find the $H.C.F$ of $\frac{324}{144},$ It is $36.$
Dividing each term of the ration by the $H.C.F$ of its terms i.e. $36,$
we get $\frac{324}{144}=\frac{324\div36}{144\div36}=\frac{9}{4}.$
Hence, the simplest form of the ratio $324 : 144$ is $9 : 4.$
View full question & answer→Question 302 Marks
Find the ratio of the following in the simplest form: $35$ minutes to $45$ minutes.
Answer$35$ minutes to $45$ minutes $= 35$ min $: 45$ min $= 7 : 9 [$diving the first-and second term by their $H.C.F = 5].$
View full question & answer→Question 312 Marks
If the sales tax on a purchase worth $Rs. 60$ is $Rs. 4.20.$ What will be the sales tax on the purchase worth $Rs. 150?$
AnswerSales tax on a purchase worth $Rs. 60 = Rs. 4.20$
Sales tax on a purchase worth $Rs. 1 = Rs. 4.2060$
Sales tax on a purchase worth $Rs. 150 = 4.2060 \times 150 = 42060 \times 100 \times 150 = Rs. 10.50$
View full question & answer→Question 322 Marks
A family of $4$ members consumes $6\ kg$ of sugar in a month. What will be the monthly consumption of sugar, if the number of family members becomes $6?$
AnswerAmount of sugar consumed by a family of $4$ members $= 6\ kg.$
View full question & answer→Question 332 Marks
Find $x$ in the following proportions: $7 : 14 = 15 : x$
Answer$7 : 14 = 15 : x$
$\frac{7}{14}=\frac{15}{\text{x}}$
$\Rightarrow\ 7\text{x}=14(15)$
$\Rightarrow\ 7\text{x}=210$
$\Rightarrow\ \text{x}=\frac{210}{7}$
$\Rightarrow\ \text{x}=30$
View full question & answer→Question 342 Marks
Give two equivalent ratios of $6 : 8.$
Answeri.e. have, $\frac{6}{8}=\frac{6\div2}{8\div2}=\frac{3}{4}$
$\therefore 3 : 4$ is an equivalent ratio of $6 : 15$
$\text{Also},\ \frac{6}{8}=\frac{6\times2}{8\times2}=\frac{12}{16}$
So, $12 : 16$ is an equivalent ratios of $6 : 8.$
Hence, $3 : 4$ and $12 : 16$ are equivalent ratios of $6 : 8.$
View full question & answer→Question 352 Marks
Set up all proportions from the numbers $9, 150, 105, 1750.$
AnswerAll proportions are:
$9 : 150 = 3 : 50$
$9 : 105 = 3 : 35$
$9 : 1750$
$150 : 105 = 10 : 7$
$150 : 1750 = 3 : 35$
$105 : 1750 = 3 : 50$
Thus, all proportions that can be formed are:
$3 : 50, 3 : 35, 10 : 7, 9 : 1750, 1750 : 9, 7 : 10, 35 : 3$ and $50 : 3$
View full question & answer→Question 362 Marks
Find the ratio of the following in the simplest form: $3$ weeks to $3$ days.
Answer$3$ weeks to $3$ days $= 3$ weeks $: 3$ days $= 21$ day $: 3$days $[1$ week $= 7$ days$] = 3 \times 7 = 3 = 7 : 1.$
View full question & answer→Question 372 Marks
A car travels $165\ km$ in $3$ hours.
How far will it travel in $7$ hours$?$
AnswerA car travels $165\ km$ in $3$ hours,
Speed of the car $=$ Distance Time $= 1653 = 55\ km/ h$
Distance travel by the car in $7$ hours $= 55 \times 7 = 385\ km.$
View full question & answer→Question 382 Marks
Find the ratio of: $3.2$ metres to $56$ metres.
Answer$3.2$ matres to $56$ matres $= 3.2 : 56 = 2 : 35 [$Dividing the first and second term by their $H.C.F = 1.6]$
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