Tag: ratio, proportion and unitary method

Questions Related to ratio, proportion and unitary method

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?

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

  1. $3 : 7$

  2. $5 : 7$

  3. $7 : 3$

  4. $7 : 5$

Show answer
Correct Option: C
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.

In each of the following questions find out the alternative which will replace the question mark.
123 : 13$^2$ :: 235 : ?

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

  1. $23^2$

  2. $35^2$

  3. $25^3$

  4. $25^2$

Show answer
Correct Option: C
Explanation:

As, $123\rightarrow 13^2$
As, $235 \rightarrow 25^3$ 
The middle digit of first term becomes power to the next term.

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 _____ .

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

  1. Rs.$5600$

  2. Rs.$3200$

  3. Rs.$9600$

  4. None of these

Show answer
Correct Option: A
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 $Rs.5600.$

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

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

  1. $15 : 8$

  2. $12 : 10$

  3. $8 : 5$

  4. $8 : 15$

Show answer
Correct Option: A
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

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

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

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

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

  1. $a = c = 1 \ and \ x \neq 0$

  2. $a = b = 0$

  3. $a = c = 0$

  4. $x _3 = 0$

  5. $ad = bc$

Show answer
Correct Option: A
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 $x \neq 0$

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

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

  1. $\displaystyle\frac{1}{3}$

  2. $\displaystyle\frac{2}{3}$

  3. $\displaystyle\frac{3}{2}$

  4. $\displaystyle\frac{3}{5}$

Show answer
Correct Option: C
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]

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.

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

  1. $3:5$

  2. $3:10$

  3. $3:15$

  4. $10:3$

Show answer
Correct Option: B
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$

Find the ratio $50$ paise to Rs. $5$

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

  1. $10:1$

  2. $1:1$

  3. $1:10$

  4. None of these

Show answer
Correct Option: C
Explanation:

Since, ${\rm{Rs}}{\rm{.1}} = {\rm{100}}\;{\rm{paise}}$

The ratio is given as,

$r = \dfrac{{50\;{\rm{paise}}}}{{5 \times 100\;{\rm{paise}}}}$

$r = \dfrac{1}{{10}}$

Thus, the required ratio is $1:10$.

Find the reduced form of the ratio of the first quantity to second quantity.
$5$ litres, $2500$ ml.

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

  1. 1:2

  2. 2:1

  3. 1:3

  4. 3:4

Show answer
Correct Option: B
Explanation:

Reduced form of $5$ liters and $2500ml$ 

in ratio
[1 liter = 1000ml so 5 liters = 5000ml]
= $\frac{{5\,liters}}{{2500ml}}\,\,\,\,\,$
= $\frac{{5000}}{{2500}}\,\,\,\,\,$
= $\frac{2}{1}\,\,\,\,\, = 2:1$

Present age of father is $42$ years and that of his son is $14$ years. Find the ratio of present age of father to the present age of son.

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

  1. 3:1

  2. 1:2

  3. 1:3

  4. 1:1

Show answer
Correct Option: A
Explanation:

$Ratio=\dfrac{Present\ age\ of\ father}{Present\ age\ of\ son.}$

            $=\dfrac{42}{14}$
$\boxed{Ratio=3:1}$