Tag: maths

Questions Related to maths

If $A\, :\, B\, =\, \displaystyle {\frac{1}{2}\, :\, \frac{3}{8},\, \, B\, :\, C\, =\, \frac{1}{3}\, :\, \frac{5}{9}\, , \, C\, :\, D\, =\, \frac{5}{6}\, :\, \frac{3}{4}}$, then the ratio $A : B : C : D$ is

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

  1. $4 : 6 : 8 : 10$

  2. $6 : 4 : 8 : 10$

  3. $6 : 8 : 9 : 10$

  4. $8 : 6 : 10 : 9$

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Correct Option: D
Explanation:

$A\, :\, B\, = \, \displaystyle {\frac{1}{2}\, :\, \frac{3}{8}\,  =\, 4\, :\, 3,}$


$B\, :\, C\, = \, \displaystyle {\frac{1}{3}\, :\, \frac{5}{9}\, =\, 3\, :\, 5,}$
$C\, :\, D\, = \, \displaystyle {\frac{5}{6}\, :\, \frac{3}{4}\, =\, 10\, :\, 9,}$ 
$\Rightarrow A : B = 4 : 3, B : C = 3 : 5 \, and \, C : D = 5 : \displaystyle \frac{9}{2}$
$\Rightarrow A : B : C : D = 4 : 3 : 5 : \displaystyle \frac{9}{2}$
$= 8 : 6 : 10 : 9$

If a : b = 3 : 4 and b : c = 5 : 9 , then a : b : c is

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

  1. 15 : 20 : 36

  2. 20 : 36 :15

  3. 3 : 20 : 9

  4. None of these

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Correct Option: A
Explanation:

To find a : b : c, b is made same in both the ratios. L.C.M of 4 and 5 is 20
$a\, :\, b\, =\, \displaystyle {\frac{3}{4}\, =\, \frac{3\, \times\, 5}{4\, \times\, 5}\, =\, \frac{15}{20}}$
$b\, :\, c\, =\, \displaystyle {\frac{5}{9}\, =\, \frac{5\, \times\, 4}{9\, \times\, 4}\, =\, \frac{20}{36}}$
$\therefore$   $ a : b : c = 15 : 20 : 36$

If a : b = 8 : 9, b : c = 18 : 40, then a : c is

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

  1. 1 : 5

  2. 5 : 2

  3. 2 : 5

  4. None of these

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Correct Option: C
Explanation:

Given a : b = 8 : 9, b : c = 18 : 40
$\displaystyle {\frac{a}{c}\, =\, \frac{a}{c}\, \times\, \frac{b}{b}\, =\, \frac{a}{b}\, \times\, \frac{b}{c}\, =\, \frac{8}{9}\, \times\, \frac{18}{40}\, =\, \frac{2}{5}}$
a : c = 2 : 5

In a class, there are $50$ boys and $30$ girls. The ratio of the number of boys to the number of girls in the class is:

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

  1. $80 : 50$

  2. $3 : 5$

  3. $5 : 3$

  4. none of the above

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Correct Option: C
Explanation:
Number of boys in class $=50$
Number of girls in class $=30$
Ratio of number of boys to the number of girls in the class $=50:30=5:3$

Two numbers are respectively 20% and 50% more than a third number The ratio of the two numbers is

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

  1. 2 : 5

  2. 3 : 5

  3. 4 : 5

  4. 6 : 7

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Correct Option: C
Explanation:

Let the third number be x.
Then first number=120% of x=$\frac{120}{100}\times x=\frac{6x}{5}$
Second number=150% of x$\frac{150}{100}\times x=\frac{3x}{2}$
$\therefore$Ratio of first two number=$\frac{6x}{5}:\frac{3x}{2}=12x:15x=4:5$

If $\displaystyle M=a\left ( m+n \right )$ and $\displaystyle N=b(m-n)$ then the value of  $\displaystyle \left ( \frac{M}{a}+\frac{N}{b} \right )\div \left ( \frac{M}{a}-\frac{N}{b} \right )$ is :

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

  1. $\displaystyle \frac{m}{n}$

  2. $\frac{n}{m}$

  3. 1


  4. $\frac{1}{2}$

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Correct Option: A
Explanation:

$\displaystyle \frac{M}{a}=m+n;\frac{N}{b}=m-n$
$\displaystyle \therefore \left ( \frac{M}{a}+\frac{N}{b} \right )\div \left ( \frac{M}{a}-\frac{N}{b} \right )=2m\div 2n=\frac{m}{n}$

If the sides of two squares are in the ratio 2:1, the ratio of the areas of the two squares will be ___________.

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

  1. 1:2

  2. 3:1

  3. 4:1

  4. 3:4

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Correct Option: C
Explanation:
Let the side of one square is $2x$ and the side of other square is $x$ of the two squares.

So, the ratio of the areas

$=\dfrac {(2x)^2}{x^2}=\dfrac{4x^2}{x^2}=\dfrac 41$ or $4:1.$

Ratio of 250ml to 2L is

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

  1. 25 : 200

  2. 8 : 1

  3. 1 : 8

  4. 120 : 300

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Correct Option: C
Explanation:

We know,

1L = 1000ml
Therefore, 2L=2000ml
Ratio = 250:2000= 1:8

The length and width of a tape are 2m and 28cm. Write their ratio.

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

  1. 100 : 14

  2. 7 : 50

  3. 50 : 7

  4. 1 : 8

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Correct Option: C
Explanation:

Length = 2m = 200 cm
 Width = 28 cm
$\dfrac{Length}{ Width}$ = $\dfrac{200}{28}$


$= \dfrac {50 }{7}$

The three quantities $a,\,b,\,c$ are said to be in continued proportion if

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

  1. $b^2=ac$

  2. $ab=c$

  3. $a+b=c$

  4. $b^2=a+c$

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Correct Option: A
Explanation:

The three quantities $a,\,b,\,c$ are said to be in continued proportion if $a:b::b:c$
$\Longrightarrow\dfrac{a}{b}=\dfrac{b}{c}$
$\Longrightarrow a\times c=b^2$
$\Longrightarrow b^2=ac$