Tag: ratio, proportion and unitary method

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Questions Related to ratio, proportion and unitary method

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

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

  1. $4$%
  2. $6\frac { 1 }{ 4 } $%
  3. $20$%
  4. $25$%
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $=\dfrac {25}{(100+25)}\times 100=20\%$

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

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

  1. $3:2$
  2. $2:3$
  3. $1:2$
  4. $2:1$
Reveal answer Fill a bubble to check yourself
B Correct answer
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
Multiple choice maths ratio, proportion and unitary method converting to ratios finding ratios other quantities

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 ____

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the property of ratios, if a/b = c/d = e/f, then each ratio is equal to (a+c+e)/(b+d+f). Adding the numerators gives 2(x+y+z) and adding the denominators gives (a+b)(x+y+z). Canceling (x+y+z) yields 2/(a+b).

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

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

  1. $\dfrac {3}{2}$
  2. $\dfrac {2}{5}$
  3. $\dfrac {3}{5}$
  4. $\dfrac {1}{5}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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

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

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?

  1. $\dfrac {4}{21}$
  2. $\dfrac {4}{5}$
  3. $\dfrac {5}{11}$
  4. $\dfrac {4}{11}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

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