Tag: other quantities

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Questions Related to other quantities

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

Sides of two similar triangles are in the ratio $4:9$.Area of these triangles are in the ratio

  1. $2:3$
  2. $4:9$
  3. $81:16$
  4. $16:81$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Given:Ratio of sides of similar triangles$=\dfrac{4}{9}$

We know that if two triangles are similar, 

ratio of areas is equal to the ratio of squares of corresponding sides.

So, $\dfrac{area \,\, of\,\, triangle\,\, 1}{area \,\, of\,\, triangle\,\, 2}=\dfrac{{\left(side\,\, of\,\, triangle\,\, 1\right)}^{2}}{{\left(side\,\, of\,\, triangle\,\, 2\right)}^{2}}$

$\dfrac{area \,\, of\,\, triangle\,\, 1}{area \,\, of\,\, triangle\,\, 2}={\left(\dfrac{4}{9}\right)}^{2}=\dfrac{16}{81}$

$\dfrac{area \,\, of\,\, triangle\,\, 1}{area \,\, of\,\, triangle\,\, 2}=\dfrac{16}{81}$

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

The ratio of the present ages of two brothers is $1:2$ and $5$ years back the ratio was $1:3$. What will be the ratio of their ages after $5$ years?

  1. $1:4$
  2. $2:3$
  3. $3:5$
  4. $5:6$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the age of the two brothers be $x$ and $y$ respectively


Given


At present 

$\dfrac { x }{ y } =\dfrac { 1 }{ 2 } \Rightarrow y=2x$

Five years ago

$\dfrac { x-5 }{ y-5 } =\dfrac { 1 }{ 3 }$

substitute $y=2x$ 

$\dfrac { x-5 }{ 2x-5 } =\dfrac { 1 }{ 3 }$

$\Rightarrow 3x-15=2x-5\Rightarrow x=10$

$\Rightarrow y=2x=2(10)=20$

$\therefore\ x=10$ and $y=20$

Required ratio:

$\displaystyle \frac { x+5 }{ y+5 } =\frac { 10+5 }{ 20+5 } =\frac { 15 }{ 25 } =\frac { 3 }{ 5 }$

Hence option (C) is the correct option.

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

A jar contains black and white marbles. If there are 25 marbles in the jar, then which of the following could not be the ratio of black to white marbles?

  1. $\dfrac{12}{13}$
  2. $\dfrac{11}{14}$
  3. $\dfrac{1}{10}$
  4. $\dfrac{8}{17}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In this Question the sum of ratio of marbles must be 25.
A. $12+13=25$
B. $11+14=25$
C. $1+10=11$
D. $8+17=25$

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

If $A\colon\,B=2\colon3,\,B\colon\,C=4\colon5\,$ and $\,C\colon\,D=6\colon7$, then $A\colon\,D=?$

  1. $\;2\colon7$
  2. $\;7\colon8$
  3. $\;16\colon35$
  4. $\;4\colon13$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given, $A:B=2:3$, $B:C=4:5$ and $C:D=6:7$


Then $\dfrac{A}{B}\times \dfrac{B}{C}=\dfrac{2}{3}\times \dfrac{4}{5}\Rightarrow \dfrac{A}{C}=\dfrac{8}{15}$

And $\dfrac{A}{C}\times \dfrac{C}{D}=\dfrac{8}{15}\times \dfrac{6}{7}$

$\Rightarrow \dfrac{A}{D}=\dfrac{16}{35}$

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

The condition for two ratios to be equal is

  1. Product of means is equal to antecedents

  2. Product of extremes is equal to consequents

  3. Antecedents are equal to consequents

  4. Product of means is equal to product of extremes
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For the ratio to be equal the product of mean =product of extremes
for ex   $\dfrac{a}{b}=\dfrac{c}{d}$
product of $a\times d=b\times c$
where
$a\times d$ $=$product of extreme.
and$b\times c$ $=$ product of means.

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$