Tag: ratio, proportion and unitary method

Questions Related to ratio, proportion and unitary method

A leak in the bottom of a tank can empty the full tank in $6$ hours. An inlet pipe fills water at the rate of $4$ litres per minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in $8$ hours, then the capacity of the tank is:

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

  1. $5260$ L

  2. $5760$ L

  3. $5846$ L

  4. $6970$ L

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Correct Option: B
Explanation:

Work done by the inlet in 1 hour $= \dfrac{1}{6}.\dfrac{1}{4}=\dfrac{1}{24}$

Work done by inlet in 1 min $=\dfrac{1}{24}\times \dfrac{1}{60}$
                                           
                                              $=\dfrac{1}{1440}$

Volume of$ \dfrac{1}{1440}$ part$ = 4$ litres
Volume of whole = $(1440 \times 4)$litres=$5760$  litres

Find the fourth proportion to $2,\,3,\,6$.

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

  1. $8$

  2. $9$

  3. $4$

  4. $6$

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Correct Option: B
Explanation:

$2:3 : :6:x$
$\Longrightarrow \dfrac{2}{3}=\dfrac{6}{x}$

$\Longrightarrow x=\dfrac{18}{2}$
$\Longrightarrow\;x=9$

The fourth proportional to $5,\,8,\,15$ is

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

  1. $24$

  2. $18$

  3. $20$

  4. $21$

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Correct Option: A
Explanation:

Let the fourth proportional to $5,\,8,\,15$ be x
$5:8::15:x$

$\Longrightarrow\;5x=8\times15$
$\Longrightarrow x=24$

The fourth proportional to $7, 11, 14$ is

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

  1. $16$

  2. $18$

  3. $20$

  4. $22$

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Correct Option: D
Explanation:
Let the fourth proportional be $x$
Therefore, $7 : 11 = 14 : x$
$\Rightarrow 7x = 11\times 14$
$\Rightarrow x = \dfrac {11\times 14}{7} = 22$
Thus fourth proportional is $22$.

The mean proportional between $234$ and $104$ is

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

  1. $12$

  2. $39$

  3. $54$

  4. None of the above

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Correct Option: D
Explanation:

Required mean proportion $=\begin{pmatrix}234\times104\end{pmatrix}^{\dfrac{1}{2}}=156$

Conall had a box of $36$ candy bars to sell for a class fundraiser. He sold $10$ of the bars on his own, and his mother sold half of the remaining bars to her coworkers. If no other bars were sold, what fraction of Conalls original $36$ bars remained unsold?

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

  1. $\cfrac{5}{8}$

  2. $\cfrac{11}{36}$

  3. $\cfrac{1}{3}$

  4. $\cfrac{13}{36}$

  5. $\cfrac{7}{18}$

Show answer
Correct Option: D
Explanation:

Given:

Number of bars Conall had $=$ $36$
After selling $10$ bars on his own,
Number of bars remaining $=$ Number of bars Conall had $-$ Number of bars he sold on his own
Number of bars remaining $=$ $36$ $-$ $10$
Number of bars remaining $=$ $26$
After his mother sold ha;f of the remaining bars,
Number of bars remained unsold $=$ Number of remaining bars $-$ Number of bars his mother sold
$=$ $26$ $-$ $\dfrac{26}{2}$
$=$ $26$ $-$ $13$
$=$ $13$
Number of bars remained unsold $=$ $13$
Fraction of Conalls bars remained unsold $=$ $\dfrac{Number \space of \space bars \space remained \space unsold}{Number \space of \space bars \space Conall \space had}$
$=$ $\dfrac{13}{36}$
Therefore, Fraction of Conalls bars remained unsold is $'$$\dfrac{13}{36}$$'$.

Find out
(i) the fourth proportional to 4, 9, 12
(ii) the third proportional to 16 and 36
(iii) the mean proportional between 0.08 and 0.18

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

  1. $27,81,0.12$

  2. $27,81,1.2$

  3. $9,27,0.12$

  4. $27,9,0.12$

Show answer
Correct Option: A
Explanation:

(i) Let the fourth proportional to $4, 9, 12$ be $x$

Then $4 : 9 : : 12 : x$
$\displaystyle \Rightarrow 4\times x=9\times 12$
$\Rightarrow x=\dfrac{9\times 12}{4}=27$
Therefore, fourth proportional to $4, 9, 12$ is $27$.
(ii) Let the third proportional to $16$ and $36$ is $x$ 
Then $16 : 36 : : 36 : x$
$\Rightarrow$ $16 \times  X = 36 \times  36$
$\displaystyle \Rightarrow  x=\frac{36\times 36}{16}=81$
Therefore, third proportional to $16$ and $36$ is $81$.
(iii) Mean proportional between $0.08$ and $0.18$
$\displaystyle =\sqrt{0.08\times 0.18}=\sqrt{\frac{8}{100}\times \frac{18}{100}}$
$\displaystyle =\sqrt{\frac{144}{100\times 100}}=\frac{12}{100}=0.12$

The third proportional to $0.36$ and $0.48$ is

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

  1. $0.64$

  2. $0.1728$

  3. $0.42$

  4. $0.94$

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Correct Option: A
Explanation:

Let the third proportional to $0.36$ and $0.48$ be x
$0.36:0.48::0.48:x$

$\Rightarrow\;x=\dfrac{0.48\times0.48}{0.36}=0.64$

In shelf, the book with green cover and that with brown cover are in the ratio $2 : 3$  there are $18$ books with green cover, then the number of books with brown cover is ?

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

  1. $12$

  2. $24$

  3. $27$

  4. $36$

Show answer
Correct Option: C
Explanation:

$Let\quad the\quad common\quad multiple\quad of\quad 2\quad and\quad 3\quad be\quad x.then:$


$ratio=2x:3x$

$it\quad is\quad given\quad that\quad books\quad with\quad green\quad color\quad are\quad 18\quad in\quad number.$

$The\quad ratio\quad is\quad 2x.$

$So\quad we\quad come\quad to\quad know\quad that:2x=18$

$x=\dfrac { 18 }{ 2 } =9$

$Ifx=9,the\quad books\quad with\quad green\quad cover=3x=3\times 9=27$

If $78$ is divided into three parts which are proportional to $1, \dfrac {1}{3}, \dfrac {1}{6}$, the middle part is

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

  1. $9\dfrac {1}{3}$

  2. $13$

  3. $17\dfrac {1}{3}$

  4. $18\dfrac {1}{3}$

Show answer
Correct Option: C
Explanation:

Given, $x + \cfrac {1}{3} x + \cfrac {1}{6}x = 78$

$\Rightarrow 9x = 468$
$\Rightarrow \cfrac {1}{3}x = \cfrac {468 }{9} \times \cfrac 13=17\cfrac {1}{3}$.