Tag: maths

Questions Related to maths

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:

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

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

Find the reduced form of the ratio of the first quantity to second quantity.
$3$ years $4$ months, $5$ years $8$ months.

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

  1. 17:10

  2. 10:17

  3. 10:15

  4. 15:10

Show answer
Correct Option: B
Explanation:

firstly year change into months

$1$ year = $12$ months 
$3$ years = 12x3 = $36$ months
$5$ years = 12x5 = $60$ months
Then reduced form are in ratio
\begin{array}{l} \frac { { 3\, years\, \, 4\, months } }{ { 5years\, \, 8\, \, months } }  \ =\frac { { \left( { 36+4 } \right) \, \, months } }{ { \left( { 60+8 } \right) \, \, months } }  \ =\frac { { 40 } }{ { 68 } }  \ =\frac { { 10 } }{ { 17 } } =10:17 \end{array}

Find the reduced form of the ratio of the first quantity to second quantity.
$7$ minutes $20$ seconds, $5$ minutes $6$ seconds.

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

  1. 111:345

  2. 234:151

  3. 220:153

  4. None

Show answer
Correct Option: C
Explanation:

Reduced form of 7 min 20 sec, 5 min 6 sec is 

firstly change minute in second 
\begin{array}{l} \frac { { 7\times 60+20 } }{ { 5\times 60+6 } }  \ =\frac { { 420+20 } }{ { 300+6 } }  \ =\frac { { 440 } }{ { 306 } }  \ =\frac { { 220 } }{ { 153 } } =220:153 \end{array}

Find the reduced form of the ratio of the first quantity to second quantity.
$3.8$ kg, $1900$ gm.

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

  1. 2:1

  2. 1:2

  3. 1:4

  4. 1:8

Show answer
Correct Option: A
Explanation:

Reduced form of $3.kg$ and $1900gm$ in ratio

firstly kg change into gms
if $1kg$  =$1000gm$
than $3.8kg$ = $3.8 \times 1000$ = $3800gm$
then, ratio 
$\frac{{3800}}{{1900}} = \frac{2}{1} = 2:1$

A class consists of 32 boys and 18 girls then the ratio of number of boys to the total number of students in the class is_____

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

  1. 16:25

  2. 25:16

  3. 9:25

  4. 25:9

Show answer
Correct Option: A
Explanation:

We have,

Number of boys $=32$

Number of girls $=18$

Then,

Total student in a class

$ =32+18 $

$ =50 $

The ratio of number of boys us

$ =\dfrac{Boys}{Total\,students} $

$ =\dfrac{32}{50} $

$ =\dfrac{16}{25} $

Hence, this is the answer.

If $A:B=2:3,B:C=4:5$ and $C:D=5:9$. then $A:D$ is equal to

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

  1. $11:17$

  2. $8:27$

  3. $5:9$

  4. $2:9$

Show answer
Correct Option: B

If $x:y=3:5$, then find $(2x+3y):(5x+7y)$.

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

  1. $\dfrac{21}{50}$

  2. $\dfrac{12}{49}$

  3. $\dfrac{11}{23}$

  4. $\dfrac{34}{46}$

Show answer
Correct Option: A

If $33\displaystyle\frac{1}{3}\%$ of $A=1.5$ of $B=\displaystyle\frac{1}{8}$ of $C$, then what is $A\,\colon\,B\,\colon\,C$?

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

  1. $5 : 3 : 2$

  2. $9 : 2 : 24$

  3. $6 : 2 : 17$

  4. None of these

Show answer
Correct Option: B
Explanation:

$33\displaystyle\frac{1}{3}\%$ of $A=1.5$ of $B=\displaystyle\frac{1}{8}$ of $C$ $\Rightarrow\displaystyle\frac{100}{3\times100}A=\displaystyle\frac{3}{2}B=\displaystyle\frac{1}{8}C\;\;\Rightarrow:\displaystyle\frac{1}{3}A=\displaystyle\frac{3}{2}B=\displaystyle\frac{1}{8}C=K:(say)$  $\Rightarrow:A=3K,\,B=\displaystyle\frac{2}{3}K,\,C=8K$  $\Rightarrow:A\,\colon\,B\,\colon\,C=3\,\colon\,\displaystyle\frac{2}{3}\,\colon\,8=3\times3\,\colon\,\displaystyle\frac{2}{3}\times3\,\colon\,8\times3=9\,\colon\,2\,\colon\,24$

If $A : B = 1 : 2, B : C = 3 : 4 , C : D = 6 : 9$ and $D : E = 12 : 16,$ then $A : B : C : D : E$ equal to

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

  1. $1 : 3 : 6 : 12 : 16$

  2. $2 : 4 : 6 : 9 : 16$

  3. $3 : 4 : 8 : 12 : 16$

  4. $3 : 6 : 8 : 12 : 16$

Show answer
Correct Option: D
Explanation:

Given,

$A : B = 1 : 2, B : C = 3 : 4 , C : D = 6 : 9$ and $D : E = 12 : 16$
$A:B=1:2=1\times 3:2\times 3=3:6$
$B:C=3:4=3\times 2:4\times 2=6:8$
$C:D=6:9=2:3=2\times 4:3\times 4=8:12$
$D:E=12:16$
Thus,
$A:B:C:D:E=3:6:8:12:16$