Tag: other quantities

Questions Related to other quantities

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. $66.67\%$

Show answer
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. $9:17$

Show answer
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

Show answer
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:

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

If a:b=$3$:$5$, find 
$\left( {10a + 3b} \right):\left( {5a + 2b} \right)$

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

  1. $9:8$

  2. $3:5$

  3. $9:5$

  4. $7:5$

Show answer
Correct Option: C
Explanation:

Given $a:b=3:5$, Let $a=3k$ and $b=5k$


Then, $(10a+3b):(5a+2b)$

$=\dfrac{10\times3k+3\times5k}{5\times3k+2\times5k}$

$=\dfrac{30k+15k}{15k+10k}$

$=\dfrac{45k}{25k}$

$=\dfrac{9}{5}$

$(10a+3b):(5a+2b)=9:5$

The total population of a village is  $3540,$  out of which  $2065$  are males. Find the ratio of males to females.

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

  1. $\dfrac 57$

  2. $\dfrac 35$

  3. $\dfrac 75$

  4. $\dfrac 65$

Show answer
Correct Option: C