Tag: equivalence of fraction, decimal fraction, percentage and ratio

Questions Related to equivalence of fraction, decimal fraction, percentage and ratio

$150$ is what percent of $30$?

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. $5\%$

  2. $20\%$

  3. $50\%$

  4. $200\%$

  5. $500\%$

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Correct Option: E
Explanation:

Let the percentage be $x$.

$\dfrac {100\%}{x\%}=\dfrac {30}{150}$
$\Rightarrow \dfrac {100}{x}\times x=\dfrac {30}{150}\times x$ .... Multiply both sides by $x$
$\Rightarrow 100=0.2x$
$\Rightarrow x=500$
Thus, $150$ is $500\%$ of $30$.

If A exceeds B by $40$ %, B is less than C by $20$% , then A : C is :

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. $28:25$

  2. $26:25$

  3. $283:251$

  4. $287:254$

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Correct Option: A
Explanation:

$\Rightarrow$  Let $C = 100.$

$\Rightarrow$   So B = 20% less than C or 80% of C = $\dfrac{80}{100}\times 100=80$
$\Rightarrow$  So, A = B + 40% of B
$\Rightarrow$   $A=80+80\times \dfrac{40}{100}=112$

$\therefore$   $A:C=\dfrac{A}{C}=\dfrac{112}{100}=\dfrac{28}{25}$

What percentage is equivalent to $\dfrac {3}{8}$ ?

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. $37.5\%$

  2. $37\%$

  3. $34.5\%$

  4. $25\%$

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Correct Option: A
Explanation:

We have to find percent of $\dfrac{3}{8}$

$\text{Percentage}=\left (\dfrac{3}{8}\times 100\right)\%$
Therefore, $\text{Percentage}=37.5\%$

What percentage is equivalent to $\dfrac {5}{8}$ ?

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. $62.5\%$

  2. $60.5\%$

  3. $625\%$

  4. $60\%$

Show answer
Correct Option: A
Explanation:

We have to find percentage of $\dfrac{5}{8}$

We know $\text{Percentage} = \dfrac{5}{8}\times 100$
Therefore, $\text{Percentage} = \dfrac{500}{8}=62.5\%$

Convert $\dfrac{46}{5}$ into percentage.

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. $92 \%$

  2. $920\%$

  3. $9.2\%$

  4. $0.92\%$

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Correct Option: B
Explanation:

The fraction in percentage equals

$\dfrac { 46 }{ 5 } \times 100=920\%$
So, option B is correct.

Amar wrote exams in four subjects-Physics, Chemistry, Biology and Social Studies. The ratio of marks he got in these exams was $2:3:4:5$. He got an aggregate of 70% in these exams. Each exam had the same maximum marks. In how many of these exams did he get more than 50%?

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. $1$

  2. $2$

  3. $3$

  4. $4$

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Correct Option: C
Explanation:

Let the maximum marks of each subject $= y$

Let the marks scored in Physics, Chemistry, Biology and social studies be $2x, \,3x, \,4x$ and $5x$.
Now, total marks scored in all 4 subjects $2x+3x+4x+5x = 14x$
Total maximum marks of all 4 subjects $=4y$
Now according to question:
$\left(\dfrac{14x}{4y}\times 100\right)\% = 70\%$
$\Rightarrow \dfrac{14x}{4y}\times 100 = 70$
$\Rightarrow y = 5x$
$\%$ age of marks scored in Physics $=\left(\dfrac{2x}{5x} \times 100\right)\% = 40\%$ 
$\%$ age of marks scored in Chemistry $=\left(\dfrac{3x}{5x} \times 100\right)\% = 60\%$ 
$\%$ age of marks scored in Biology $=\left(\dfrac{4x}{5x} \times 100\right)\% = 80\%$
$\%$ age of marks scored in Social Studies $=\left(\dfrac{5x}{5x} \times 100\right)\% = 100\%$  
So, he got more than $50\%$ in Chemistry, Biology and Social Studies.
Hence, the answer is $3$.

270 candidates appeared for an examination, of which 252 passed. The pass percentage is? 

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. $80 \%$

  2. $83 \frac { 1 } { 2 } \%$

  3. $90 \frac { 1 } { 3 } \%$

  4. $93 \frac { 1 } { 3 } \%$

Show answer
Correct Option: D
Explanation:

Total candidates = 270

Passes candidates = 252
Passed percentage = $\dfrac{252}{270} \times 100\%=93.33\%=93\dfrac{1}{3}\%$

Which one of the following shows the best percentage? 

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. $\dfrac { 384 } { 540 }$

  2. $\dfrac { 425 } { 500 }$

  3. $\dfrac { 570 } { 700 }$

  4. $\dfrac { 480 } { 660 }$

Show answer
Correct Option: B
Explanation:
$(a)\dfrac{384}{540}=\dfrac{384}{540}\times 100\%=71\dfrac{1}{9}\%$

$(b)\dfrac{425}{500}=\dfrac{425}{500}\times 100\%=85\%$

$(c)\dfrac{570}{700}=\dfrac{570}{700}\times 100\%=81\dfrac{3}{7}\%$

$(d)\dfrac{480}{660}=\dfrac{480}{660}\times 100\%=72\dfrac{8}{11}\%$

$\dfrac{425}{500}$ shows the best percentage.

What percent of a day is 3 hours? 

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. $12 \frac { 1 } { 2 } \%$

  2. $16 \frac { 1 } { 3 } \%$

  3. $18 \frac { 2 } { 3 } \%$

  4. $22 \frac { 1 } { 2 } \%$

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Correct Option: A
Explanation:

No . of hours in a day $24hours$

Percentage of $3$ hrs is given as 

$\dfrac{3}{24}\times 100$

$\dfrac 18\times 100=12\frac 12\%$

Express the following ratios as percentages: 

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. 5 : 4

  2. 1 : 1

  3. 2 : 3

  4. 9 : 16

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Correct Option: A