Question 12 Marks
Write the ratio of first quantity to second quantity in the reduced form : 1.5 kg, 2500 gm
Answer1.5 kg, 2500 gm
1.5 kg = 1.5 x 1000 gm = 1500gm
$\begin{aligned} \text { Ratio }=\frac{1.5 kg }{2500 gm } & =\frac{1500 gm }{2500 gm } \\ & =\frac{1500}{2500} \\ & =\frac{15}{25} \\ & =\frac{5 \times 3}{5 \times 5}=\frac{3}{5} \\ & =3: 5\end{aligned}$
View full question & answer→Question 22 Marks
Write the ratio of first quantity to second quantity in the reduced form : 4 sq.m, 800 sq.cm
Answer4 sq.m, 800 sq.cm
4 sq.m = 4 x 10000 sq.cm = 40000 sq.cm
$\begin{aligned} \text { Ratio }=\frac{4 \text { sq.m }}{800 sq \cdot cm } & =\frac{40000 sq \cdot cm }{800 sq \cdot cm } \\ & =\frac{40000}{800} \\ & =\frac{400}{8} \\ & =\frac{8 \times 50}{8 \times 1}=\frac{50}{1} \\ & =50: 1\end{aligned}$
View full question & answer→Question 32 Marks
Write the ratio of first quantity to second quantity in the reduced form : 5 dozen, 120 units
Answer5 dozen, 120 units
5 dozen = 5 x 12 units = 60 units
$\begin{aligned} \text { Ratio }=\frac{5 \text { dozen }}{120 \text { units }} & =\frac{60 \text { units }}{120 \text { units }} \\ & =\frac{60}{120} \\ & =\frac{60 \times 1}{60 \times 2}=\frac{1}{2} \\ & =1: 2\end{aligned}$
View full question & answer→Question 42 Marks
Write the ratio of first quantity to second quantity in the reduced form : ₹ 17, ₹ 25 and 60 paise
Answer₹ 17, ₹ 25 and 60 paise
₹ 17 = 17 x 100 paise = 1700 paise
₹ 25 and 60 paise = (25x 100) paise + 60 paise
= (2500 + 60) paise
= 2560 paise
$\begin{aligned} \text { Ratio } & =\frac{₹ 17}{₹ 25 \text { and } 60 \text { paise }} \\ & =\frac{1700 \text { paise }}{2560 \text { paise }} \\ & =\frac{1700}{2560} \\ & =\frac{20 \times 85}{20 \times 128} \\ & =\frac{85}{128} \\ & =85: 128\end{aligned}$
View full question & answer→Question 52 Marks
Write the ratio of first quantity to second quantity in the reduced form : 1024 MB, 1.2 GB [(1024 MB = 1GB)]
Answer1024 MB, 1.2 GB
1024 MB = 1 GB
$\begin{aligned} \text { Ratio }=\frac{1024 MB }{1.2 GB } & =\frac{1 GB }{1.2 GB }=\frac{1}{1.2} \\ & =\frac{10}{12}=\frac{2 \times 5}{2 \times 6} \\ & =\frac{5}{6} \\ & =5: 6\end{aligned}$
View full question & answer→Question 62 Marks
Convert the following ratios into percentages : $\frac{144}{1200}$
Answer$\begin{array}{ll}& \text { Let } \frac{144}{1200}=x \% \\ \therefore & \frac{144}{1200}=\frac{x}{100} \\ \therefore & x=\frac{144}{1200} \times 100=\frac{144}{12}=12 \% \\ \therefore & \frac{144}{1200}=12 \%\end{array}$
View full question & answer→Question 72 Marks
Convert the following ratios into percentages : $\frac{5}{16}$
AnswerLet $\frac{5}{16}=x \%$
$\begin{array}{ll}
\therefore & \frac{5}{16}=\frac{x}{100} \\
\therefore & x=\frac{5}{16} \times 100=\frac{5}{4} \times 25=31.25 \% \\
\therefore & \frac{5}{16}=31.25 \%
\end{array}$
View full question & answer→Question 82 Marks
Convert the following ratios into percentages : $\frac{22}{30}$
AnswerLet $\frac{22}{30}=x \%$
$\begin{array}{ll}
\therefore & \frac{22}{30}=\frac{x}{100} \\
\therefore & x=\frac{22}{30} \times 100=\frac{22}{3} \times 10=73.33 \% \\
\therefore & \frac{22}{30}= 7 3 . 3 3 \%
\end{array}$
View full question & answer→Question 92 Marks
Convert the following ratios into percentages : $\quad \frac{5}{8}$
AnswerLet $\frac{5}{8}=x \%$
$ \therefore \quad \frac{5}{8}=\frac{x}{100}$
$\therefore \quad x=\frac{5}{8} \times 100=\frac{5}{2} \times 25=62.5 \%$
$\therefore \quad \frac{5}{8}=62.5 \%$
View full question & answer→Question 102 Marks
Convert the following ratios into percentages : $37: 500$
AnswerLet $37 : 500 = x\%$
$\therefore \frac{37}{500}=\frac{x}{100}$
$\therefore x=\frac{37}{500} \times 100=\frac{37}{5}=7.4 \%$
$\therefore 37: 500=7.4 \%$
View full question & answer→Question 112 Marks
Write the following ratios in the reduced form $:$ The ratio of numbers denoting perimeter to area of a square, having side $4\ cm.$
AnswerThe ratio of numbers denoting perimeter to area of a square, having side $4\ cm.$ side of square $= 4\ cm$
Perimeter of square $= 4 \times $ side $= 4 \times 4 = 16\ cm$
Area of square $= (side)^2 = (4)^2 = 16\ cm^2$
Ratio of numbers denoting perimeter to area of square
$=\frac{\text { Perimeter of the square }}{\text { Area of the square }}$
$=\frac{16}{16}=\frac{1}{1}=1: 1 $
$\therefore$ The ratio of numbers denoting perimeter to area of a square is $1: 1$.
View full question & answer→Question 122 Marks
Write the following ratios in the reduced form : The ratio of diagonal to the length of a rectangle, having length 4 cm and breadth 3 cm.
AnswerThe ratio of diagonal to the length of a rectangle, having length 4 cm and breadth 3 cm.
Let $\square ABCD$ be a rectangle.
In $\triangle A B C, \angle B=90^{\circ}$
$\left.A C^2=A B^2+B C^2 \ldots \text { [Pythagoras theorem }\right]$
$=4^2+3^2=16+9$
$\therefore A C^2=25$
$AC =5$... [Taking square root on both side]
The ratio of diagonal to the length of a rectangle $=\frac{A C}{A B}=\frac{5}{4}=5: 4$
$\therefore$ The ratio of diagonal to the length of a rectangle is $5: 4$ View full question & answer→Question 132 Marks
Write the following ratios in the reduced form $:$ Radius to the diameter of a circle.
AnswerRadius to the diameter of a circle.
Let radius of the circle be $r$
then, diameter $= 2 \times $ radius $= 2r$
Ratio of radius to diameter of circle
$=\frac{\text { Radius of the circle }}{\text { Diameter of the circle }}$
$=\frac{r}{2 r}$
$=\frac{1}{2}$
$=1: 2$
$\therefore$ Ratio of radius to diameter of circle is $1: 2$.
View full question & answer→Question 142 Marks
If $a, b, c$ are in continued proportion then show that, $\frac{(a+b)^2}{a b}=\frac{(b+c)^2}{b c}$.
Answer$a, b, c$ are in continued proportion. Let $\frac{a}{b}=\frac{b}{c}=k$.
$\therefore b=c k, \quad a=b k=c k \times k=c k^2$
Substituting values of $a$ and $b$.
$ \text { LHS }=\frac{(a+b)^2}{a b}=\frac{\left(c k^2+c k\right)^2}{\left(c k^2\right)(c k)}=\frac{c^2 k^2(k+1)^2}{c^2 k^3}=\frac{(k+1)^2}{k}$
$\text { RHS }=\frac{(b+c)^2}{b c}=\frac{(c k+c)^2}{(c k) c}=\frac{c^2(k+1)^2}{c^2 k}=\frac{(k+1)^2}{k}$
$\therefore \text { LHS }=\text { RHS. } \quad \therefore \frac{(a+b)^2}{a b}=\frac{(b+c)^2}{b c}$
View full question & answer→Question 152 Marks
If $\frac{a}{b}=\frac{c}{d}$ then show that $\frac{5 a-3 c}{5 b-3 d}=\frac{7 a-2 c}{7 b-2 d}$
AnswerLet $\frac{a}{b}=\frac{c}{d}=k \quad \therefore a=b k, c=d k$
Substituting values of $a$ and $c$ in both sides,
$
\begin{array}{c}
\text { LHS }=\frac{5 a-3 c}{5 b-3 d}=\frac{5(b k)-3(d k)}{5 b-3 d}=\frac{k(5 b-3 d)}{(5 b-3 d)}=k \\
\text { RHS }=\frac{7 a-2 c}{7 b-2 d}=\frac{7(b k)-2(d k)}{7 b-2 d}=\frac{k(7 b-2 d)}{7 b-2 d}=k \\
\therefore \text { LHS }=\text { RHS. } \\
\therefore \frac{5 a-3 c}{5 b-3 d}=\frac{7 a-2 c}{7 b-2 d}
\end{array}
$
View full question & answer→Question 162 Marks
$\text {if 5x then find the value of the ratio } \frac{3 x^2+y^2}{3 x^2-y^2}$
Answer$
\begin{array}{rlrl}
\frac{x}{y} & =\frac{4}{5} \\
\frac{x^2}{y^2} & =\frac{16}{25} \\
\frac{3 x^2}{y^2} & =\frac{48}{25} & \\
\therefore \quad \frac{3 x^2+y^2}{3 x^2-y^2} & \left.=\frac{48+25}{48-25} \quad \text {...(multiplying both sides by } 3\right) \\
\therefore \quad \frac{3 x^2+y^2}{3 x^2-y^2} & =\frac{73}{23}
\end{array}
$
View full question & answer→Question 172 Marks
If $\frac{x}{y}=\frac{4}{5}$ then find the value of the ratio $\frac{4 x-y}{4 x+y}$.
Answer$
\begin{array}{c}
\frac{x}{y}=\frac{4}{5} \\
\frac{4 x}{y}=\frac{16}{5}\quad \ldots \text { (multiplying both sides by 4) } \\
\therefore \frac{4 x+y}{4 x-y}=\frac{16+5}{16-5} \quad \quad \ldots \text { (using componendo-dividendo) } \\
\therefore \frac{4 x+y}{4 x-y}=\frac{21}{11} \\
\therefore \frac{4 x-y}{4 x+y}=\frac{11}{21} \\
\end{array}
$
View full question & answer→Question 182 Marks
If $\frac{a}{b}=\frac{7}{4}$ then find the ratio $\frac{5 a-b}{b}$.
Answer$\quad \frac{a}{b}=\frac{7}{4}$
$
\therefore \quad \frac{a}{7}=\frac{b}{4} \quad \ldots \text { (using alternando) }
$
Let $\frac{a}{7}=\frac{b}{4}=m$
$
\begin{aligned}
\therefore a & =7 m, \quad b=4 m \\
\therefore \frac{5 a-b}{b} & =\frac{5(7 m)-4 m}{4 m} \\
& =\frac{35 m-4 m}{4 m} \\
& =\frac{31}{4}
\end{aligned}
$
View full question & answer→Question 192 Marks
If $\frac{a}{b}=\frac{5}{3}$ then find the ratio $\frac{a+7 b}{7 b}=$.
AnswerMethod I
If $\frac{a}{b}=\frac{5}{3}$ then $\frac{a}{5}=\frac{b}{3}=k$, ...(using alternando)
$
\begin{aligned}
& \therefore a=5 k, b=3 k \\
& \therefore \frac{a+7 b}{7 b}=\frac{5 k+7 \times 3 k}{7 \times 3 k} \\
& =\frac{5 k+21 k}{21 k} \\
& =\frac{26 k}{21 k}=\frac{26}{21} \\
\end{aligned}
$
View full question & answer→Question 202 Marks
The ratio of expenditure and income of Mahesh is 3 : 5. Find the percentage of expenses to
his income.
AnswerThe ratio of expenditure to income is $3: 5$. To convert it into a percentage, convert the second term into 100.
$\frac{3}{5}=\frac{3 \times 20}{5 \times 20}=\frac{60}{100} \quad \therefore \frac{\text { Expenditure }}{\text { Income }}=\frac{60}{100}=60 \% \quad \therefore$ Mahesh spends $60 \%$ of his income.
View full question & answer→Question 212 Marks
The length of a rectangular field is 1.2 km and its breadth is 400 metre. Find the ratio
of length to breadth.
AnswerHere the length is in kilometers and the breadth is in meters. In order to find the ratio of length to breadth, they must be expressed in the same unit. Hence we convert kilometres to meters.
$
1.2 \mathrm{~km}=1.2 \times 1000=1200 \mathrm{~m}
$
$\therefore$ ratio of $1200 \mathrm{~m}$, to $400 \mathrm{~m}$ is $\frac{1200}{400}=\frac{3}{1}$, that is $3: 1$
View full question & answer→Question 222 Marks
If $\frac{a}{b}=\frac{7}{3}$, then find the values of the following ratios : $\frac{7 a+9 b}{7 a-9 b}$
Answer$\frac{a}{b}=\frac{7}{3}$
...[Given]
$ \therefore \quad \frac{a}{b} \times \frac{7}{9}=\frac{7}{3} \times \frac{7}{9} $
$\therefore \quad\left[\text { Multiplying both sides by } \frac{7}{9}\right]$
$\therefore \quad \frac{7 a}{9 b}=\frac{49}{27}$
$\therefore \quad \frac{7 a+9 b}{7 a-9 b}=\frac{49+27}{49-27}$
$\therefore \quad \frac{7 a+9 b}{7 a-9 b}=\frac{76}{22}=\frac{2 \times 38}{2 \times 11}=\frac{38}{11}$
$\therefore \quad \frac{7 a+9 b}{7 a-9 b}=38: 11$
View full question & answer→Question 232 Marks
If $\frac{a}{b}=\frac{7}{3}$, then find the values of the following ratios : $\frac{a^3-b^3}{b^3}$
Answer$\frac{ a }{ b }=\frac{7}{3}$
$\therefore \quad\left(\frac{a}{b}\right)^3=\left(\frac{7}{3}\right)^3$
$\therefore \quad \frac{ a ^3}{ b ^3}=\frac{343}{27}$
$\therefore \quad \frac{a^3-b^3}{ b ^3}=\frac{343-27}{27}$
$\therefore \quad \frac{a^3-b^3}{b^3}=\frac{316}{27}$
$\therefore \quad \frac{a^3-b^3}{b^3}=316: 27$
View full question & answer→Question 242 Marks
If $\frac{a}{b}=\frac{7}{3}$, then find the values of the following ratios : $\frac{2 a^2+3 b^2}{2 a^2-3 b^2}$
Answer$ \quad \frac{a}{b}=\frac{7}{3}$
$\therefore \quad\left(\frac{a}{b}\right)^2=\left(\frac{7}{3}\right)^2 \quad \ldots \text { [Given] }$
$\therefore \quad \frac{ a ^2}{ b ^2}=\frac{49}{9}$
$\therefore \quad \frac{ a ^2}{ b ^2} \times \frac{2}{3}=\frac{49}{9} \times \frac{2}{3}$
$\therefore \quad \frac{2 a ^2}{3 b ^2}=\frac{98}{27}$
$\therefore \quad \frac{2 a ^2+3 b ^2}{2 a ^2-3 b ^2}=\frac{98+27}{98-27}$
$\therefore \quad \frac{2 a ^2+3 b ^2}{2 a ^2-3 b ^2}=\frac{125}{71}$
$\therefore \quad \frac{2 a ^2+3 b ^2}{2 a ^2-3 b ^2}=125: 71$
View full question & answer→Question 252 Marks
If $\frac{a}{b}=\frac{7}{3}$, then find the values of the following ratios : $\frac{5 a+3 b}{5 a-3 b}$
Answer$\text { i. } \quad \frac{a}{b}=\frac{7}{3}$
$\therefore \quad \frac{a}{b} \times \frac{5}{3}=\frac{7}{3} \times \frac{5}{3}$
$\therefore \quad \ldots\left[\text { Multiplying both sides by } \frac{5}{3}\right]$
$\therefore \quad \frac{5 a}{3 b}=\frac{35}{9}$
$\therefore \quad \frac{5 a+3 b}{5 a-3 b}=\frac{35+9}{35-9}$
$\therefore \quad \frac{5 a+3 b}{5 a-3 b}=\frac{44}{26}$
$\therefore \quad \frac{5 a+3 b}{5 a-3 b}=22: 13$
$\therefore \quad \frac{2 \times 22}{2 \times 13}=\frac{22}{13}$
Alternate wethod:
$\frac{ a }{ b }=\frac{7}{3}$
Let the common multiple be $m$.
then, $a=7 m$ and $b =3 m$
$\begin{aligned}
\therefore \quad \frac{5 a+3 b}{5 a-3 b} & =\frac{5(7 m )+3(3 m )}{5(7 m )-3(3 m )} \\
& =\frac{35 m +9 m }{35 m -9 m }=\frac{44 m }{26 m }=\frac{44}{26} \\
& =\frac{2 \times 22}{2 \times 13}=\frac{22}{13} \\
\therefore \quad \frac{5 a+3 b}{5 a-3 b} & =22: 13
\end{aligned}$
View full question & answer→Question 262 Marks
Compare the following : $\quad \frac{9.2}{5.1}, \frac{3.4}{7.1}$
Answer$\begin{array}{ll}\quad & \frac{9.2}{5.1}, \frac{3.4}{7.1} \\ & 9.2 \times 7.1=65.32 \\ & 5.1 \times 3.4=17.34 \\ & \text { Here, } 65.32>17.34 \\ \therefore \quad & \frac{9.2}{5.1}>\frac{3.4}{7.1}\end{array}$
View full question & answer→Question 272 Marks
Compare the following : $\frac{\sqrt{80}}{\sqrt{48}}, \frac{\sqrt{45}}{\sqrt{27}}$
Answer$\begin{array}{ll}
& \frac{\sqrt{80}}{\sqrt{48}}, \frac{\sqrt{45}}{\sqrt{27}} \\
& \sqrt{80} \times \sqrt{27}=\sqrt{2160} \\
& \sqrt{48} \times \sqrt{45}=\sqrt{2160} \\
& \text { Here, } 2160=2160 \\
\therefore \quad & \sqrt{2160}=\sqrt{2160} \\
\therefore \quad & \frac{\sqrt{80}}{\sqrt{48}}=\frac{\sqrt{45}}{\sqrt{27}}
\end{array}$
Alternate method:
$\frac{\sqrt{80}}{\sqrt{48}}, \frac{\sqrt{45}}{\sqrt{27}}$
Consider, $\frac{\sqrt{80}}{\sqrt{48}}=\frac{\sqrt{16 \times 5}}{\sqrt{16 \times 3}}=\frac{4 \sqrt{5}}{4 \sqrt{3}}=\frac{\sqrt{5}}{\sqrt{3}}$
$\frac{\sqrt{45}}{\sqrt{27}}=\frac{\sqrt{9 \times 5}}{\sqrt{9 \times 3}}=\frac{3 \sqrt{5}}{3 \sqrt{3}}=\frac{\sqrt{5}}{\sqrt{3}}$
Here, $\frac{\sqrt{5}}{\sqrt{3}}=\frac{\sqrt{5}}{\sqrt{3}}$
$\therefore \quad \frac{\sqrt{80}}{\sqrt{48}}=\frac{\sqrt{45}}{\sqrt{27}}$
View full question & answer→Question 282 Marks
Compare the following : $\frac{5}{18}, \frac{17}{121}$
Answer$\begin{array}{ll}\quad & \frac{5}{18}, \frac{17}{121} \\ & 5 \times 121=605 \\ & 18 \times 17=306 \\ & \text { Here, } 605>306 \\ \therefore \quad & \frac{5}{18}>\frac{17}{121}\end{array}$
View full question & answer→Question 292 Marks
Compare the following : $\frac{3 \sqrt{5}}{5 \sqrt{7}}, \frac{\sqrt{63}}{\sqrt{125}}$
Answer$\begin{aligned}
\frac{3 \sqrt{5}}{5 \sqrt{7}}, \frac{\sqrt{63}}{\sqrt{125}} & \\
3 \sqrt{5} \times \sqrt{125} & =3 \times \sqrt{5 \times 125} \\
& =3 \times \sqrt{5 \times 25 \times 5} \\
& =3 \times 5 \times 5 \\
& =3 \times 25=75 \\
5 \sqrt{7} \times \sqrt{63} & =5 \times \sqrt{7 \times 63} \\
& =5 \times \sqrt{7 \times 9 \times 7} \\
& =5 \times 3 \times 7=105
\end{aligned}$
Here, $75<105$
$\therefore \quad \frac{3 \sqrt{5}}{5 \sqrt{7}}<\frac{\sqrt{63}}{\sqrt{125}}$
View full question & answer→Question 302 Marks
Compare the following : $\quad \frac{\sqrt{5}}{3}, \frac{3}{\sqrt{7}}$
Answer$\begin{array}{ll}\quad & \frac{\sqrt{5}}{3}, \frac{3}{\sqrt{7}} \\ & \sqrt{5} \times \sqrt{7}=\sqrt{35} \\ & 3 \times 3=9=\sqrt{9^2}=\sqrt{81} \\ & \text { Here, } 35<81 \\ \therefore \quad & \sqrt{35}<\sqrt{81} \\ \therefore \quad & \frac{\sqrt{5}}{3}<\frac{3}{\sqrt{7}}\end{array}$
View full question & answer→Question 312 Marks
Find the following ratios : The lengths of sides of a rectangle are $5 cm$ and $3.5 cm$. Find the ratio of numbers denoting its perimeter to area.
AnswerLength of rectangle = (l) = $5 cm,$
Breadth of rectangle = (b) =$ 3.5 cm$
Perimeter of the rectangle = $2(l + b)$
$= 2(5 + 3.5)$
$= 2 x 8.5$
$= 17 cm$
Area of the rectangle = l x b
$= 5 x 3.5$
$= 17.5 cm^2$
Ratio of numbers denoting perimeter to the area of rectangle
$\begin{aligned}
& =\frac{\text { perimeter }}{\text { area }} \\
& =\frac{17}{17.5} \\
& =\frac{17 \times 10}{17.5 \times 10} \\
& =\frac{170}{175} \\
& =\frac{5 \times 34}{5 \times 35} \\
& =\frac{34}{35} \\
& =34: 35
\end{aligned}$
$\therefore$ Ratio of numbers denoting perimeter to the area of rectangle is $34: 35$.
View full question & answer→Question 322 Marks
Find the following ratios $:$ The ratio of diagonal of a square to its side, if the length of side is $7\ cm.$
AnswerLength of side of square $= 7\ cm$
$\therefore$ Diagonal of square $= \sqrt2 \times$ side
$= \sqrt{2} \times 7$
$= 7 \sqrt{2}\ cm$
Ratio of diagonal of a square to its side
$ =\frac{\text { diagonal }}{\text { side }}$
$=\frac{7 \sqrt{2}}{7}$
$=\frac{\sqrt{2}}{1}$
$=\sqrt{2}: 1$
$\therefore$ The ratio of diagonal of a square to its side is $\sqrt{ 2} : 1$.
View full question & answer→Question 332 Marks
Find the following ratios $:$ The ratio of circumference of circle with radius $r$ to its area.
AnswerLet the radius of the circle is $r.$
$\therefore$ circumference $= 2\pi r$ and area $= \pi r^2$
Ratio of circumference to the area of circle
$=\frac{\text { circumference }}{\text { area }}$
$=\frac{2 \pi r }{\pi r ^2}$
$=\frac{2}{ r }$
$=2: r$
$\therefore$ The ratio of circumference of circle with radius $r$ to its area is $2: r$.
View full question & answer→Question 342 Marks
Find the following ratios $:$ The ratio of radius to circumference of the circle.
AnswerLet the radius of circle be $r.$
then, its circumference $= 2\pi r$
Ratio of radius to circumference of the circle
$ =\frac{\text { radius }}{\text { circumference }}$
$=\frac{ r }{2 \pi r }$
$=\frac{1}{2 \pi}$
$=1: 2 \pi $
The ratio of radius to circumference of the circle is $1: 2 \pi$.
View full question & answer→Question 352 Marks
Three persons can build a small house in 8 days. To build the same house in 6 days, how many persons are required?
AnswerLet the persons required to build a house in 6 days be x.
Days required to build a house and number of persons are in inverse proportion.
∴ 6 × x = 8 × 3
∴ 6 x = 24
∴ x = 4
∴ 4 persons are required to build the house in 6 days.
View full question & answer→Question 362 Marks
Find the reduced form of the ratio of the first quantity to second quantity : 7 minutes 20 seconds, 5 minutes 6 seconds
Answer7 minutes 20 seconds, 5 minutes 6 seconds
7 minutes 20 seconds = 7 x 60 seconds + 20 seconds
= (420 + 20) seconds
= 440 seconds
5 minutes 6 seconds = 5 x 60 seconds + 6 seconds
= (300 + 6) seconds
= 306 seconds
$\begin{aligned} \therefore \quad \text { Ratio } & =\frac{7 \text { minutes } 20 \text { seconds }}{5 \text { minutes } 6 \text { seconds }}=\frac{440 \text { seconds }}{306 \text { seconds }} \\ & =\frac{440}{306}=\frac{2 \times 220}{2 \times 153}=\frac{220}{153}= 2 2 0 : 1 5 3 \end{aligned}$
View full question & answer→Question 372 Marks
Find the reduced form of the ratio of the first quantity to second quantity : 3.8 kg, 1900 gm
Answer3.8 kg, 1900 gm
3.8 kg = 3.8 x 1000 gm = 3800 gm
$\begin{aligned} \therefore \quad \text { Ratio } & =\frac{3.8 kg }{1900 gm }=\frac{3800 gm }{1900 gm }=\frac{3800}{1900} \\ & =\frac{1900 \times 2}{1900 \times 1}=\frac{2}{1}= 2 : 1 \end{aligned}$
View full question & answer→Question 382 Marks
Find the reduced form of the ratio of the first quantity to second quantity : 3 years 4 months, 5 years 8 months
Answer3 years 4 months, 5 years 8 months
3 years 4 months = 3×12 months + 4 months
= (36 + 4) months
= 40 months
5 years 8 months = 5 x 12 months + 8 months
= (60 + 8) months
= 68 months
$\begin{aligned} \therefore \quad \text { Ratio } & =\frac{3 \text { years } 4 \text { months }}{5 \text { years } 8 \text { months }}=\frac{40 \text { months }}{68 \text { months }}=\frac{40}{68} \\ & =\frac{4 \times 10}{4 \times 17}=\frac{10}{17}=10: 17\end{aligned}$
View full question & answer→Question 392 Marks
Find the reduced form of the ratio of the first quantity to second quantity : 5 litres, 2500 ml
Answer5 litres, 2500 ml
5 litres = 5 x 1000 ml = 5000ml
$\begin{aligned} \therefore \quad \text { Ratio } & =\frac{5 \text { litres }}{2500 ml }=\frac{5000 ml }{2500 ml }=\frac{5000}{2500} \\ & =\frac{2500 \times 2}{2500 \times 1}=\frac{2}{1}=2: 1\end{aligned}$
View full question & answer→Question 402 Marks
Find the reduced form of the ratio of the first quantity to second quantity : ₹ 14, ₹ 12 and 40 paise
Answer₹ 14, ₹12 and 40 paise
₹ 14 = 14 x 100 paise = 1400 paise
₹ 12 and 40 paise = 12 x 100 paise + 40 paise
= (1200 + 40) paise
= 1240 paise
$\begin{aligned} \therefore \quad \text { Ratio } & =\frac{₹ 14}{₹ 12 \text { and } 40 \text { paise }}=\frac{1400 \text { paise }}{1240 \text { paise }} \\ & =\frac{1400}{1240}=\frac{40 \times 35}{40 \times 31}=\frac{35}{31}= 3 5 : 3 1 \end{aligned}$
View full question & answer→Question 412 Marks
Find the reduced form of the ratio of the first quantity to second quantity $: ₹ 700, ₹ 308$
Answer$\text { ₹ 700, ₹ } 308$
$\text { Ratio }=\frac{700}{308}=\frac{28 \times 25}{28 \times 11}=\frac{25}{11}=25: 11$
View full question & answer→