Tag: converting to ratios

Questions Related to converting to ratios

Find the reduced form of the ratio of the first quantity to second quantity.
$3.8$ kg, $1900$ gm.

maths ratio, proportion and unitary method converting to ratios finding ratios other quantities

  1. 2:1

  2. 1:2

  3. 1:4

  4. 1:8

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Correct Option: A
Explanation:

Reduced form of $3.kg$ and $1900gm$ in ratio

firstly kg change into gms
if $1kg$  =$1000gm$
than $3.8kg$ = $3.8 \times 1000$ = $3800gm$
then, ratio 
$\frac{{3800}}{{1900}} = \frac{2}{1} = 2:1$

A class consists of 32 boys and 18 girls then the ratio of number of boys to the total number of students in the class is_____

maths ratio, proportion and unitary method converting to ratios finding ratios other quantities

  1. 16:25

  2. 25:16

  3. 9:25

  4. 25:9

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Correct Option: A
Explanation:

We have,

Number of boys $=32$

Number of girls $=18$

Then,

Total student in a class

$ =32+18 $

$ =50 $

The ratio of number of boys us

$ =\dfrac{Boys}{Total\,students} $

$ =\dfrac{32}{50} $

$ =\dfrac{16}{25} $

Hence, this is the answer.

If $A:B=2:3,B:C=4:5$ and $C:D=5:9$. then $A:D$ is equal to

maths ratio, proportion and unitary method converting to ratios finding ratios other quantities

  1. $11:17$

  2. $8:27$

  3. $5:9$

  4. $2:9$

Show answer
Correct Option: B

If $x:y=3:5$, then find $(2x+3y):(5x+7y)$.

maths ratio, proportion and unitary method converting to ratios finding ratios other quantities

  1. $\dfrac{21}{50}$

  2. $\dfrac{12}{49}$

  3. $\dfrac{11}{23}$

  4. $\dfrac{34}{46}$

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Correct Option: A

If $33\displaystyle\frac{1}{3}\%$ of $A=1.5$ of $B=\displaystyle\frac{1}{8}$ of $C$, then what is $A\,\colon\,B\,\colon\,C$?

maths ratio, proportion and unitary method converting to ratios finding ratios other quantities

  1. $5 : 3 : 2$

  2. $9 : 2 : 24$

  3. $6 : 2 : 17$

  4. None of these

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Correct Option: B
Explanation:

$33\displaystyle\frac{1}{3}\%$ of $A=1.5$ of $B=\displaystyle\frac{1}{8}$ of $C$ $\Rightarrow\displaystyle\frac{100}{3\times100}A=\displaystyle\frac{3}{2}B=\displaystyle\frac{1}{8}C\;\;\Rightarrow:\displaystyle\frac{1}{3}A=\displaystyle\frac{3}{2}B=\displaystyle\frac{1}{8}C=K:(say)$  $\Rightarrow:A=3K,\,B=\displaystyle\frac{2}{3}K,\,C=8K$  $\Rightarrow:A\,\colon\,B\,\colon\,C=3\,\colon\,\displaystyle\frac{2}{3}\,\colon\,8=3\times3\,\colon\,\displaystyle\frac{2}{3}\times3\,\colon\,8\times3=9\,\colon\,2\,\colon\,24$

If $A : B = 1 : 2, B : C = 3 : 4 , C : D = 6 : 9$ and $D : E = 12 : 16,$ then $A : B : C : D : E$ equal to

maths ratio, proportion and unitary method converting to ratios finding ratios other quantities

  1. $1 : 3 : 6 : 12 : 16$

  2. $2 : 4 : 6 : 9 : 16$

  3. $3 : 4 : 8 : 12 : 16$

  4. $3 : 6 : 8 : 12 : 16$

Show answer
Correct Option: D
Explanation:

Given,

$A : B = 1 : 2, B : C = 3 : 4 , C : D = 6 : 9$ and $D : E = 12 : 16$
$A:B=1:2=1\times 3:2\times 3=3:6$
$B:C=3:4=3\times 2:4\times 2=6:8$
$C:D=6:9=2:3=2\times 4:3\times 4=8:12$
$D:E=12:16$
Thus,
$A:B:C:D:E=3:6:8:12:16$

If $\displaystyle\frac{a}{b}=\displaystyle\frac{7}{9},\displaystyle\frac{b}{c}=\displaystyle\frac{3}{5}$, then what is the value of $a\,\colon\,b\,\colon\,c$?

maths ratio, proportion and unitary method converting to ratios finding ratios other quantities

  1. $7:9:15$

  2. $9:7:15$

  3. $7:9:14$

  4. $1:9:15$

Show answer
Correct Option: A
Explanation:

Given, $\dfrac{a}{b}=\dfrac{7}{9}$ and$\dfrac{b}{c}=\dfrac{3}{5}$
Then $\displaystyle \frac{a}{b}\times \frac{b}{c}=\frac{7}{9}\times \dfrac{3}{5}\Rightarrow \frac{a}{c}=\frac{7}{15}$
$\Rightarrow \dfrac{b}{c}=\dfrac{3}{5}=\dfrac{9}{15}$
$\Rightarrow a:b=7:9$ and $b:c=9:15$

$\Rightarrow \dfrac{a}{b}:\dfrac{b}{c}=\dfrac{7}{9}:\dfrac{9}{15}$
In this $9$ is common. 
Then $ a:b:c=7:9:15$

If $A\,\colon\,B=\displaystyle\frac{1}{2}\colon\displaystyle\frac{1}{3},\,B\,\colon\,C=\displaystyle\frac{1}{2}\colon\displaystyle\frac{1}{3}$, then $A\,\colon\,B\,\colon\,C$ is equal to:

maths ratio, proportion and unitary method converting to ratios finding ratios other quantities

  1. $\;2\,\colon\,3\,\colon\,3$

  2. $\;1\,\colon\,2\,\colon\,6$

  3. $\;3\,\colon\,2\,\colon\,6$

  4. $\;9\,\colon\,6\,\colon\,4$

Show answer
Correct Option: D
Explanation:

$\;A\,\colon\,B=\displaystyle\frac{1}{2} \colon\displaystyle\frac{1}{3}=\displaystyle\frac{1}{2}\times6\ \colon\displaystyle\frac{1}{3}\times6=3\,\colon\,2$


$\;\;\;\;\;\;\;\;B\,\colon\,C=\displaystyle\frac{1}{2}\colon\displaystyle\frac{1}{3}=3\,\colon\,2$

By taking the L.C.M. of $2$ and $3$, i.e., $6$, we can make the value of $B$ equal in both the ratio.

$\;\;\;\;\;\;\;\;\displaystyle\frac{A}{B}=\displaystyle\frac{3}{2}=\displaystyle\frac{9}{6}$ and $\displaystyle\frac{B}{C}=\displaystyle\frac{3}{2}=\displaystyle\frac{6}{4}$

$\;\;\;\;\;\;\;\therefore\,A\,\colon\,B\,\colon\,C=9\,\colon\,6\,\colon\,4$.

The ratio of two numbers is a : b. If one of them is x then other is 

maths ratio, proportion and unitary method converting to ratios finding ratios other quantities

  1. $\displaystyle \frac{ab}{x}$

  2. $\displaystyle \frac{b}{ax}$

  3. $\displaystyle \frac{b}{a+b}x$

  4. $\displaystyle \frac{bx}{a}$

Show answer
Correct Option: D
Explanation:

Let the required number be y
$a : b : : x : y$
$a \times y = b \times x$
$\displaystyle y=\frac{bx}{a}$

If $a:b = \displaystyle \frac {2}{9} : \frac {1}{3}, b:c = \frac {2}{7}: \frac {5}{14} , d:c = \frac {7}{10} : \frac {3}{5},$ then find $a :b:c:d$.

maths ratio, proportion and unitary method converting to ratios finding ratios other quantities

  1. $2 : 12 : 28 : 30$

  2. $10 : 12 : 18 : 39$

  3. $16 : 24 : 30 : 35$

  4. $9 : 18 : 20 : 31$

Show answer
Correct Option: C
Explanation:

$\displaystyle \frac {a}{b} = \frac {2}{9} \div \frac {1}{3}=  \frac {2}{9} \times \frac {3}{1}, \frac {b}{c}= \frac {2}{7} \div \frac {5}{14} = \frac {2}{7} \times \frac {14}{5}= \frac {4}{5}$

$\displaystyle \frac {d}{c}=\frac {7}{10} \div \frac {3}{5} = \frac {7}{10} \times \frac {5}{3} = \frac {7}{6} \Rightarrow \frac {c}{d} = \frac {6}{7} \Rightarrow a = \frac {2b}{3}, c= \frac {5b}{4}, d= \frac {7c}{6}=\frac {7}{6} \times \frac {5b}{4} = \frac {35b}{24}$
$\therefore a:b:c:d = \displaystyle \frac {2b}{3}: b : \frac {5b}{4}\times 24 : \frac {35b}{24} = 16 : 24: 30 : 35.$