Q: Are the ratio \$1 : 2\$ and \$2 : 3\$ equivalent ?

To check this, we need to know whether\$\displaystyle \frac{1}{2}= \frac{2}{3}\$We have, \$\displaystyle \frac{1}{2}=\frac{1\times 3}{2\times 3}\$\$\displaystyle =\frac{3}{6}\$and \$\cfrac{2}{3}=\cfrac{2\times 2}{3\times 2}=\cfrac{4}{6}\$We find that\$\displaystyle \frac{3}{6}< \frac{4}{6},\$ which means that \$\displaystyle \frac{1}{2}< \frac{2}{3}.\$Therefore, The ratio \$1 : 2\$ is not equivalent to the ratio \$2 : 3 \$

Q: A ratio equivalent to \$2:5\$ is

The simplest form of ratio \$6 : 15 =2\times 3:5\times 3= 2 : 5\$So, \$2 : 5\$ is equivalent to \$6 : 15\$

Q: The greatest ratio among the ratios \$2:3\$, \$5:8\$, \$75:121\$ and \$40:25\$ is

\$\textbf{Step 1: Convert the fractions with same denominators.}\$Given ratios,\$2: 3=\frac{2}{3}\$ \$5: 8=\frac{5}{8}\$ \$75: 121=\frac{75}{121}\$ \$40: 25=\frac{40}{25}\$Finding the LCM of the denominators by prime factorisation, we get\$\begin{array}{l|l}2 & 3,8,121,25 \\\hline 2 & 3,4,121,25 \\\hline 2 & 3,2,121,25 \\\hline 3 & 3,1,121,25 \\\hline 5 & 1,1,121,25 \\\hline 5 & 1,1,121,5 \\\hline 11 & 1,1,121,1 \\\hline 11 & 1,1,11,1 \\\hline & 1,1,1,1 \\\hline\end{array}\$\$\begin{aligned}\text {LCM of } 3,8,121,25=& 2 \times 2 \times 2 \times 3 \times 5 \times 5 \times 11 \times 11 \\&=72600\end{aligned}\$Converting the fractions with same denominators, we get\$\begin{aligned}&2: 3=\frac{2}{3}=\frac{2 \times 24200}{3 \times 24200}=\frac{48400}{72600} \\&5: 8=\frac{5}{8}=\frac{5 \times 9075}{8 \times 9075}=\frac{45375}{72600} \\&75: 121=\frac{75}{121}=\frac{75 \times 600}{121 \times 600}=\frac{45000}{72600} \\&40: 25=\frac{40}{25}=\frac{40 \times 2904}{25 \times 2904}=\frac{116160}{72600}\end{aligned}\$\$\textbf{Step 2: Find the fraction with the greatest numerator.}\$Since all the denominators of the fractions are same, the fraction with the greatest numerator will be the greatest.\$\therefore \frac{116160}{72600}\$ is the greatest fraction\$\Rightarrow 40: 25\$ is the greatest ratio.\$\therefore \textbf{Option D is correct}\$

Q: Which of the following ratios is the largest?

We have get the value then\$(A)7:15=\dfrac{7}{15}=0.46\$\$(B)15:23=\dfrac{15}{23}=0.65\$\$(C)17:25=\dfrac{17}{25}=0.68\$\$(D)21:29=\dfrac{21}{29}=0.72\$Then option (D) 21:29 is the largest ratio

Q: Which ratio is greater?\$7 : 8\$ or \$2 : 3\$.

In two or more ratios, wherever the numerator and denominator differs by one, the ratio with higher numerator is always the greater one.\$7:8=\dfrac{7}{8}=0.875\$\$2:3=\dfrac{2}{3}=0.67\$\$\therefore \dfrac{7}{8}>\dfrac{2}{3}\$

Q: Compare the following pair of ratios:\$\frac{5}{18},\frac{17}{121}\$

\$5*121=605\$\$18*17=306\$Now, \$605>306\$\$\dfrac{5}{18}>\dfrac{17}{121}\$

Q: Write the ratio of radius to the diameter of a circle.

Let diameter \$=d\$Then radius \$=r= d/2\$Ratio \$=\dfrac{radius }{ diameter }= \dfrac{d/2}{d}= \dfrac{1}{2}\$

Q: Mark the correct alternative of the following.A ratio equivalent to \$2:3\$ is

Given the ratio is \$2:3\$.Now,\$\dfrac{6}{9}\$\$=\dfrac{2\times 3}{3\times 3}\$\$=\dfrac{2}{3}\$.So the equivalent ratio is \$6:9\$.

Q: A multistory building has 25 floors above the ground level each of height \$5 \mathrm{m}\$. It also has 3 floors in the basement each of height \$5 \mathrm{m}\$. A lift in building moves at a rate of \$1 \mathrm{m} / \mathrm{s}\$. If a man starts from \$50 \mathrm{m}\$ above the ground, how long will it take him to reach at \$2^{\text {nd }}\$ floor of the basement?

Each floor has the height of \$5 \mathrm{m}\$ and basement of \$3\$ floors.If a man starts from \$50 \mathrm{m}\$ above ground and reached at \$2^{\text {nd }}\$ floor of basement. Distance traveled above basement \$=50\ m\$And below basement \$=2\times5=10\ m\$Total distance traveled=\$(50+10) \mathrm{m}=60 \mathrm{m}\$Rate of moving of a lift \$=1 \mathrm{m} / \mathrm{s}\$ that is in \$1\$ second it moves \$1\$ metre.So, time taken to reach \$60\$ metre \$=60\times 1=60\ s\$Hence, a man reaches at \$2^{\text {nd }}\$ floor of basement in \$60\$ seconds.

Q: In a ratio \$3:4\$, if the antecedent is \$12\$, then the consequent is

\$\dfrac{3}{4}=\dfrac{12}{x}\;\$\$\Rightarrow\;3x=48\$\$x=16\$

Question 1

Are the ratio $1 : 2$ and $2 : 3$ equivalent ?

Accepted Answer

To check this, we need to know whether$\displaystyle \frac{1}{2}= \frac{2}{3}$We have, $\displaystyle \frac{1}{2}=\frac{1\times 3}{2\times 3}$$\displaystyle =\frac{3}{6}$and $\cfrac{2}{3}=\cfrac{2\times 2}{3\times 2}=\cfrac{4}{6}$We find that$\displaystyle \frac{3}{6}< \frac{4}{6},$ which means that $\displaystyle \frac{1}{2}< \frac{2}{3}.$Therefore, The ratio $1 : 2$ is not equivalent to the ratio $2 : 3 $

Question 2

A ratio equivalent to $2:5$ is

Accepted Answer

The simplest form of ratio $6 : 15 =2\times 3:5\times 3= 2 : 5$So, $2 : 5$ is equivalent to $6 : 15$

Question 3

The greatest ratio among the ratios $2:3$, $5:8$, $75:121$ and $40:25$ is

Accepted Answer

$\textbf{Step 1: Convert the fractions with same denominators.}$Given ratios,$2: 3=\frac{2}{3}$     $5: 8=\frac{5}{8}$   $75: 121=\frac{75}{121}$  $40: 25=\frac{40}{25}$Finding the LCM of the denominators by prime factorisation, we get$\begin{array}{l|l}2 & 3,8,121,25 \\hline 2 & 3,4,121,25 \\hline 2 & 3,2,121,25 \\hline 3 & 3,1,121,25 \\hline 5 & 1,1,121,25 \\hline 5 & 1,1,121,5 \\hline 11 & 1,1,121,1 \\hline 11 & 1,1,11,1 \\hline & 1,1,1,1 \\hline\end{array}$$\begin{aligned}\text {LCM of } 3,8,121,25=& 2 \times 2 \times 2 \times 3 \times 5 \times 5 \times 11 \times 11 \&=72600\end{aligned}$Converting the fractions with same denominators, we get$\begin{aligned}&2: 3=\frac{2}{3}=\frac{2 \times 24200}{3 \times 24200}=\frac{48400}{72600} \&5: 8=\frac{5}{8}=\frac{5 \times 9075}{8 \times 9075}=\frac{45375}{72600} \&75: 121=\frac{75}{121}=\frac{75 \times 600}{121 \times 600}=\frac{45000}{72600} \&40: 25=\frac{40}{25}=\frac{40 \times 2904}{25 \times 2904}=\frac{116160}{72600}\end{aligned}$$\textbf{Step 2: Find the fraction with the greatest numerator.}$Since all the denominators of the fractions are same, the fraction with the greatest numerator will be the greatest.$\therefore \frac{116160}{72600}$ is the greatest fraction$\Rightarrow 40: 25$ is the greatest ratio.$\therefore  \textbf{Option D is correct}$

Question 4

Which of the following ratios is the largest?

Accepted Answer

We have get the value then$(A)7:15=\dfrac{7}{15}=0.46$$(B)15:23=\dfrac{15}{23}=0.65$$(C)17:25=\dfrac{17}{25}=0.68$$(D)21:29=\dfrac{21}{29}=0.72$Then option (D) 21:29 is the largest ratio

Question 5

Which ratio is greater?$7 : 8$ or $2 : 3$.

Accepted Answer

In two or more ratios, wherever the numerator and denominator differs by one, the ratio with higher numerator is always the greater one.$7:8=\dfrac{7}{8}=0.875$$2:3=\dfrac{2}{3}=0.67$$\therefore \dfrac{7}{8}>\dfrac{2}{3}$

Question 6

Compare the following pair of ratios:$\frac{5}{18},\frac{17}{121}$

Accepted Answer

$5*121=605$$18*17=306$Now, $605>306$$\dfrac{5}{18}>\dfrac{17}{121}$

Question 7

Write the ratio of radius to the diameter of a circle.

Accepted Answer

Let diameter $=d$Then radius $=r= d/2$Ratio $=\dfrac{radius }{ diameter }= \dfrac{d/2}{d}= \dfrac{1}{2}$

Question 8

Mark the correct alternative of the following.A ratio equivalent to $2:3$ is

Accepted Answer

Given the ratio is $2:3$.Now,$\dfrac{6}{9}$$=\dfrac{2\times 3}{3\times 3}$$=\dfrac{2}{3}$.So the equivalent ratio is $6:9$.

Question 9

A multistory building has 25 floors above the ground level each of height $5 m$ . It also has 3 floors in the basement each of height $5 m$ . A lift in building moves at a rate of $1 m / s$ .
If a man starts from $50 m$ above the ground, how long will it take him to reach at $2^{nd}$ floor of the basement?

Medium

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Accepted Answer

Each floor has the height of $5 \mathrm{m}$ and basement of $3$ floors.If a man starts from $50 \mathrm{m}$ above ground and reached at $2^{\text {nd }}$ floor of basement. Distance traveled above basement $=50\ m$And below basement $=2\times5=10\ m$Total distance traveled=$(50+10) \mathrm{m}=60 \mathrm{m}$Rate of moving of a lift $=1 \mathrm{m} / \mathrm{s}$ that is in $1$ second it moves $1$ metre.So, time taken to reach $60$ metre $=60\times 1=60\ s$Hence, a man reaches at $2^{\text {nd }}$ floor of basement in $60$ seconds.

Question 10

In a ratio $3:4$, if the antecedent is $12$, then the consequent is

Accepted Answer

$\dfrac{3}{4}=\dfrac{12}{x}\;$$\Rightarrow\;3x=48$$x=16$

Revise with Concepts

Comparing Quantities using Ratio

Learn with Videos

Quick Summary With Stories

Introduction to Ratios

Equivalent Ratios

Finding the value of Multiple Units

Ratios in Proportion

Are the ratio $1 : 2$ and $2 : 3$ equivalent ?

A ratio equivalent to $2 : 5$ is

The greatest ratio among the ratios $2 : 3$ , $5 : 8$ , $75 : 121$ and $40 : 25$ is

Which of the following ratios is the largest?

Which ratio is greater?
$7 : 8$ or $2 : 3$ .

Compare the following pair of ratios:
$\frac{5}{1 8}, \frac{1 7}{1 2 1}$

Write the ratio of radius to the diameter of a circle.

Mark the correct alternative of the following.
A ratio equivalent to $2 : 3$ is

In a ratio $3 : 4$ , if the antecedent is $12$ , then the consequent is

Revise with Concepts

Comparing Quantities using Ratio

Learn with Videos

Quick Summary With Stories

Introduction to Ratios

Equivalent Ratios

Finding the value of Multiple Units

Ratios in Proportion

Are the ratio 1:2 and 2:3 equivalent ?

A ratio equivalent to 2:5 is

The greatest ratio among the ratios 2:3, 5:8, 75:121 and 40:25 is

Which of the following ratios is the largest?

Which ratio is greater? 7:8 or 2:3.

Compare the following pair of ratios: 185​,12117​

Write the ratio of radius to the diameter of a circle.

Mark the correct alternative of the following. A ratio equivalent to 2:3 is

A multistory building has 25 floors above the ground level each of height 5m. It also has 3 floors in the basement each of height 5m. A lift in building moves at a rate of 1m/s. If a man starts from 50m above the ground, how long will it take him to reach at 2nd floor of the basement?

In a ratio 3:4, if the antecedent is 12, then the consequent is

Are the ratio $1 : 2$ and $2 : 3$ equivalent ?

A ratio equivalent to $2 : 5$ is

The greatest ratio among the ratios $2 : 3$ , $5 : 8$ , $75 : 121$ and $40 : 25$ is

Which ratio is greater?
$7 : 8$ or $2 : 3$ .

Compare the following pair of ratios:
$\frac{5}{1 8}, \frac{1 7}{1 2 1}$

Mark the correct alternative of the following.
A ratio equivalent to $2 : 3$ is

In a ratio $3 : 4$ , if the antecedent is $12$ , then the consequent is