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

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

  1. $4 : 6 : 8 : 10$
  2. $6 : 4 : 8 : 10$
  3. $6 : 8 : 9 : 10$
  4. $8 : 6 : 10 : 9$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

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


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

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

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

  1. 15 : 20 : 36

  2. 20 : 36 :15

  3. 3 : 20 : 9

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
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$

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

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

  1. 2 : 5

  2. 3 : 5

  3. 4 : 5

  4. 6 : 7
Reveal answer Fill a bubble to check yourself
C Correct answer
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=$\frac{6x}{5}:\frac{3x}{2}=12x:15x=4:5$

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

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 :

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

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

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