Tag: ratio, proportion and unitary method

Quizzes (5) Questions (125)

Questions Related to ratio, proportion and unitary method

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

In what ratio must a grocer mix two varieties of pulses costing Rs.$15$ and Rs.$20$ per kg respectively so as to get a mixture worth Rs.$16.50$ kg?

  1. $3 : 7$
  2. $5 : 7$
  3. $7 : 3$
  4. $7 : 5$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Consider the amount of pulse of price $Rs15$ $=x$


And the amount of pulse of price $Rs20$ $=y$

Then the total amount of mixture $=15x+20y$

But the price per $kg$ of mixture $=Rs16.50$

So, total price of $x+y kg$ $=16.50(x+y)$

Now according to the equation 

$16.50(x+y)=15x+20y$

$16.50x+16.50y=15x+20y$

$1.50x=3.50y$

$\frac { x }{ y } =\frac { 3.50 }{ 1.50 } \ =\frac { 0.7 }{ 0.3 } =\frac { 7 }{ 3 } $

Hence, required Ratio is $7:3$

So, the Option $C$ is the correct answer.

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

A certain amount was divided between Kavita and Reena in the ratio $4 : 3$.If Reena's share was Rs.$2400$ , then the total amount is _____ .

  1. Rs.$5600$
  2. Rs.$3200$
  3. Rs.$9600$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
$\Rightarrow$  Ratio of Kavita and Reena amount is $4:3$.
$\Rightarrow$  Let their shares be $Rs. 4x$ and $Rs. 3x.$
$\Rightarrow$  Then, $3x = 2400$
$\Rightarrow$ $x=800$
 $\therefore$  Total amount = $4x+3x=7x=Rs.(7\times 800)=Rs.5600$
$\therefore$  The total amount is $Rs.5600.$
Multiple choice maths ratio, proportion and unitary method converting to ratios finding ratios other quantities

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

  1. $15 : 8$
  2. $12 : 10$
  3. $8 : 5$
  4. $8 : 15$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given: $\dfrac{A}{B}=\dfrac{2}{3}$


$\Rightarrow B=\dfrac{3A}{2}$


Now, $\dfrac{B}{C}=\dfrac{4}{5}$
putting the value of B in terms of A we get

$\Rightarrow \dfrac{3A}{2C}=\dfrac{4}{5}$

$\Rightarrow \dfrac{C}{A}=\dfrac{15}{8}$

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

If $b \neq d$, the fractions $\dfrac{ax + b}{cx + d}$ and $\dfrac{b}{d}$ are unequal if:

  1. $a = c = 1 \ and \ x \neq 0$
  2. $a = b = 0$
  3. $a = c = 0$
  4. $x _3 = 0$
  5. $ad = bc$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\cfrac { ax+b }{ cx+d } \neq \cfrac { b }{ d } \Longrightarrow adx+bd\neq bcx+bd\Longrightarrow (ad-bc)x\neq 0\ \therefore x\neq 0\quad and\quad ad\neq bc$

We know, $b \neq d$
$\therefore a=c=1$
$\therefore a=c=1 $ and $x \neq 0$

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

Given that $\displaystyle\frac{4p + 9q}{p} = \frac{5q}{p - q}$ and $p$ and $q$ are both positive. calculate $\displaystyle\frac{p}{q}$

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

Given 

$\dfrac{4p+9q}{p}=\dfrac{5q}{p-q}$
or, $4p^2-4pq+9pq-9q^2=5pq$
or, $4p^2=9q^2$
or, $\dfrac{p}{q}=\dfrac{3}{2}$ [Since $p$ and $q$ are both positive]

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

The length and breadth of a rectangular field are $50\ m$ and $15\ m$ respectively. Find the ratio of the breadth to the length of the field.

  1. $3:5$
  2. $3:10$
  3. $3:15$
  4. $10:3$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The length of the rectangular field is $50 m$ and breadth of the field is $15 m$.

The ratio of breadth and length is,

${\rm{breadth}}:{\rm{length}} = 15:50=\dfrac{15}{50}=\dfrac{3}{10}$

$ = 3:10$