Tag: ratio, proportion and unitary method

Questions Related to ratio, proportion and unitary method


select the missing number based on the given
$27: 65 :: 54: $____

maths ratio, proportion and unitary method more on proportion terms related to proportion proportion

  1. $130$

  2. $127$

  3. $126$

  4. $125$

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Correct Option: A
Explanation:

$let\> the\> missing\> number\> be \>x \\ then\> (\frac{27}{65})=(\frac{54}{x})\\  \>x=(\frac{54\times 65}{27})\\= 130$

A dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains $25$%. The percentage of water in the mixture is

maths ratio, proportion and unitary method more on proportion terms related to proportion proportion

  1. $4$%

  2. $6\frac { 1 }{ 4 } $%

  3. $20$%

  4. $25$%

Show answer
Correct Option: C
Explanation:

According to the question,

Let's assume milkman has $100$ liter of milk, If he added $x$ liter of water, the percentage of water in the mixture$=\dfrac {x}{(100+x)}\times 100$

The milk gain $25$%, he must have added $25$ liter water in $100$ liter of milk. Then the percentage of water in the mixture$=\dfrac {25}{(100+25)}\times 100=20\%$


In the new mixture, If the milk is $80$% then $80$% of total mixture should be $100$ liter
$(100+x)\times \dfrac{80}{100}=100$
$8x=200$
$x=25$

Then, the percentage of water in the mixture $=\dfrac {25}{(100+25)}\times 100=20\%$

Convert the following into percentage.
$\dfrac{2}{3}$.

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

  1. $66\%$

  2. $65\%$

  3. $33\%$

  4. $66.67\%$

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Correct Option: D
Explanation:
$\dfrac{2}{3}$ into percentage
$=\dfrac{2}{3}\times 100\%= \dfrac{200}{3}\% = 66.67\%$

Convert the following into percentage.
$\dfrac{5}{8}$.

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

  1. $62.5 \%$

  2. $65.5\%$

  3. $66.6\%$

  4. $64\%$

Show answer
Correct Option: A
Explanation:
$\dfrac{5}{8}$
$=\dfrac{5}{8}\times 100\%=\dfrac{500}{8}\%=62.5\%$

If $\dfrac{1}{x} + y = 3$ and $x + \dfrac{1}{y} = 2$ then $x:y$ is 

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

  1. $3:2$

  2. $2:3$

  3. $1:2$

  4. $2:1$

Show answer
Correct Option: B
Explanation:
The question states '...then x: is' 
It should state '..then x:y is'

Given
$\dfrac { 1 }{ x } +y=3$ --- Eqn (1)
$x+\dfrac { 1 }{ y } =2$ ---Eqn (2)

Multiplying Eqn (1) by x and Eqn (2) by y, we get:

$x\left( \dfrac { 1 }{ x } +y \right) =3x\quad \Rightarrow 1+yx=3x$ --- Eqn (3)
$y\left( x+\dfrac { 1 }{ y }  \right) =2y\quad \Rightarrow xy+1=2y$ --- Eqn (4)

Subtracting Eqn (4) and Eqn (5), we get:

$1+yx-1-yx=3x-2y$
$\Rightarrow 0=3x-2y$
$\Rightarrow 3x=2y$
$\Rightarrow \dfrac { x }{ y } =\dfrac { 2 }{ 3 } $
$\therefore x:y=2:3$

Hence the answer is B

Find the ratio of: $36$ to $64$

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

  1. $9:11$

  2. $9:12$

  3. $9:16$

  4. $9:17$

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Correct Option: C
Explanation:

$\dfrac{36}{64}=\dfrac{36\div 4}{64\div 4} =\dfrac{9}{16}$

The ratio of $40\ min$ to $2.5$ hours is

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

  1. $4:17$

  2. $4:18$

  3. $4:13$

  4. $4:15$

Show answer
Correct Option: D
Explanation:
$\dfrac {40\ min}{2.5\ hr}$
$=\dfrac {10\ min}{2hr +30\ min}=\dfrac {40}{2\times 60+30}$
$=\dfrac {40}{150}\ \Rightarrow \boxed {4:15}$
Option $D$ is correct

If ${x+y}{ax+by}=\dfrac{y+z}{ay+bz}=\dfrac{z+x}{az+bx}$, then "each of these ratio is equal to $\dfrac{2}{a+b}$, unless $x+y+z=0$." this statement is ____

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

  1. True

  2. False

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Correct Option: A

$30$ cricket players and $20$ kho-kho players are training on a field. What is the ratio cricket players to the total number of players?

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

  1. $\dfrac {3}{2}$

  2. $\dfrac {2}{5}$

  3. $\dfrac {3}{5}$

  4. $\dfrac {1}{5}$

Show answer
Correct Option: C
Explanation:

$\dfrac{\text{number of cricket players}}{\text{total number of players}}=\dfrac{30}{30+20}=\dfrac{30}{50} =\dfrac{3}{5}$

Snehal has a red ribbon that is $80cm$ long and a blue ribbon, $220m$ long. What is the ratio of the length of the red ribbon to that of the blue ribbon?

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

  1. $\dfrac {4}{21}$

  2. $\dfrac {4}{5}$

  3. $\dfrac {5}{11}$

  4. $\dfrac {4}{11}$

Show answer
Correct Option: D
Explanation:

$\dfrac{\text{length of red ribbon}}{\text{length of blue ribbon}}= \dfrac{80cm}{220cm} = \dfrac{8}{22} = \dfrac{4}{11}$