Tag: converting to ratios

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Questions Related to converting to ratios

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

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

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

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

  1. $\dfrac 57$
  2. $\dfrac 35$
  3. $\dfrac 75$
  4. $\dfrac 65$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total population is 3540 and males are 2065. Females = 3540 - 2065 = 1475. The ratio of males to females is 2065/1475. Dividing both by 295 gives 7/5.