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Quantitative Aptitude

PERCENTAGE MCQs

Percentages

Total Questions : 2296 | Page 5 of 230 pages
Question 41.

A batsman scored 110 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?

  1.    45%
  2.     \(45\frac{5}{11}\)%
  3.     \(54\frac{6}{11}\) %
  4.    55%
 Discuss Question
Answer: Option B. ->  \(45\frac{5}{11}\)%

Number of runs made by running = 110 - (3 x 4 + 8 x 6)


= 110 - (60)


= 50.


So, Required percentage =  \(\left(\frac{50}{110}\times100\right)\) % =  \(45\frac{5}{11}\) %

Question 42.

Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are:

  1.    39, 30
  2.    41, 32
  3.    42, 33
  4.    43, 34
 Discuss Question
Answer: Option C. -> 42, 33

Let their marks be (x + 9) and x.


Then, x + 9 = \(\frac{56}{100}\left(x+9+x\right)\)


 25(x + 9) = 14(2x + 9)


 3x = 99


 x = 33


So, their marks are 42 and 33.


 

Question 43.

A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:

  1.    588 apples
  2.    600 apples
  3.    672 apples
  4.    700 apples
 Discuss Question
Answer: Option D. -> 700 apples

Suppose originally he had x apples.


Then, (100 - 40)% of x = 420.


\(\frac{60}{100}\times x = 420\)


x =  \(\left(\frac{420\times100}{60}\right)= 700.\)

Question 44.

What percentage of numbers from 1 to 70 have 1 or 9 in the units digit?

  1.    1
  2.    14
  3.    20
  4.    21
 Discuss Question
Answer: Option C. -> 20

the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.


Number of such number =14


So, Required percentage =    \(\left(\frac{14}{70}\times100\right)\)  % =   20%

Question 45.

If A = x% of y and B = y% of x, then which of the following is true?

  1.    A is smaller than B.
  2.    A is greater than B
  3.    Relationship between A and B cannot be determined.
  4.    If x is smaller than y, then A is greater than B.
  5.    None of these
 Discuss Question
Answer: Option E. -> None of these

x% of y =      \(\left(\frac{x}{100}\times y\right) = \left(\frac{y}{100}\times x\right)\)   = y% of x


 So, A=B.

Question 46.

If 20% of a = b, then b% of 20 is the same as:

  1.    4% of a
  2.    5% of a
  3.    20% of a
  4.    None of these
 Discuss Question
Answer: Option A. -> 4% of a

20% of a = b      \(\Rightarrow\frac{20}{100}a = b\)


 So, b% of 20 =     \(\left(\frac{b}{100}\times 20\right) = \left(\frac{20}{100}a\times\frac{1}{100}\times20\right)\)    = 4% of a.

Question 47.

In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is \(\frac{2}{3} \) of the number of students of 8 years of age which is 48. What is the total number of students in the school?

  1.    72
  2.    80
  3.    120
  4.    150
  5.    100
 Discuss Question
Answer: Option E. -> 100

Let the number of students be x. Then,


Number of students above 8 years of age = (100 - 20)% of x = 80% of x.


     So, 80% of x = 48 + \(\frac{2}{3} of 48\)


\(\frac{80x}{100} = 80\)


x = 100

Question 48.

Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.


 

  1.    2 : 3
  2.    1 : 1
  3.    3 : 4
  4.    4 : 3
 Discuss Question
Answer: Option D. -> 4 : 3

5% of A + 4% of B =  (6% of A + 8% of B)\(\frac{2}{3}\) 


= \(\frac{5}{100}A + \frac{5}{100}B = \frac{2}{3}\left(\frac{6}{100}A + \frac{8}{100}B\right)\)


= \(\frac{1}{100}A +\frac{1}{100}B =\frac{1}{25}A + \frac{1}{75}B\)


= \(\left(\frac{1}{20}-\frac{1}{25}\right)A =\left(\frac{4}{75}- \frac{1}{25}\right)B\)


= \(\frac{1}{100}A =\frac{1}{75}B\)


\(\frac{A}{B} =\frac{100}{75}=\frac{4}{3 }.\)


So,  Required ratio = 4:3.

Question 49.

A student multiplied a number by \(\frac{3}{5}\)  instead of  \(\frac{5}{3}\)  What is the percentage error in the calculation

  1.    34%
  2.    44%
  3.    54%
  4.    64%
 Discuss Question
Answer: Option D. -> 64%

Let the number be x.


Then, error =  \(\frac{3}{5}x-\frac{5}{3}x=\frac{16}{15}x.\)


Error% =  \(\left(\frac{16x}{15}\times\frac{3}{5}x\times100\right)\) % = 64%


 

Question 50.

In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was:

  1.    2700
  2.    2900
  3.    3000
  4.    3100
 Discuss Question
Answer: Option A. -> 2700

Number of valid votes = 80% of 7500 = 6000.


 Valid votes polled by other candidate = 45% of 6000


\(\left(\frac{45}{100}\times6000\right) = 2700.\)

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