Percentage

Percentage

Important Formulas




  1. Concept of Percentage:By a certain percent, we mean that many hundredths.

    Thus, x percent means x hundredths, written as x%.













    To express x% as a fraction: We have, x% = x .
    100















        Thus, 20% = 20 = 1 .
    100 5




















    To express a as a percent: We have, a = a x 100 %.
    b b b


















        Thus, 1 = 1 x 100 % = 25%.
    4 4


  2. Percentage Increase/Decrease:If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is:













    R x 100 %
    (100 + R)

    If the price of a commodity decreases by R%, then the increase in consumption so as not to decrease the expenditure is:














    R x 100 %
    (100 – R)


  3. Results on Population:Let the population of a town be P now and suppose it increases at the rate of R% per annum, then:















    1. Population after n years = P 1 + R n
    100











    2. Population n years ago = P














    1 + R n
    100



  4. Results on Depreciation:Let the present value of a machine be P. Suppose it depreciates at the rate of R% per annum. Then:















    1. Value of the machine after n years = P 1 – R n
    100











    2. Value of the machine n years ago = P














    1 – R n
    100















    3. If A is R% more than B, then B is less than A by R x 100 %.
    (100 + R)














    4. If A is R% less than B, then B is more than A by R x 100 %.
    (100 – R)






1

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?
A. 45% B.
45 5 %
11
C.
54 6 %
11
D. 55%

View Answer


Answer: Option B


Explanation:


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


= 110 – (60)


= 50.


















Required percentage = 50 x 100 % = 45 5 %
110 11

2.

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:
A. 39, 30 B. 41, 32
C. 42, 33 D. 43, 34

View Answer


Answer: Option C


Explanation:


Let their marks be (x + 9) and x.













Then, x + 9 = 56 (x + 9 + x)
100

25(x + 9) = 14(2x + 9)


3x = 99


x = 33


So, their marks are 42 and 33.


3.

A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:
A. 588 apples B. 600 apples
C. 672 apples D. 700 apples

View Answer


Answer: Option D


Explanation:


Suppose originally he had x apples.


Then, (100 – 40)% of x = 420.













60 x x = 420
100













x = 420 x 100   = 700.
60

4.

What percentage of numbers from 1 to 70 have 1 or 9 in the unit’s digit?
A. 1 B. 14
C. 20 D. 21

View Answer


nswer: Option C


Explanation:


Clearly, the numbers which have 1 or 9 in the unit’s digit, have squares that end in 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















Required percentage = 14 x 100 % = 20%.
70

5.

If A = x% of y and B = y% of x, then which of the following is true?
A. A is smaller than B. B. A is greater than B
C. Relationship between A and B cannot be determined. D. If x is smaller than y, then A is greater than B.
E. None of these

View Answer


Answer: Option E


Explanation:






















x% of y = x x y = y x x = y% of x
100 100

A = B.


6.

If 20% of a = b, then b% of 20 is the same as:
A. 4% of a B. 5% of a
C. 20% of a D. None of these

View Answer


Answer: Option A


Explanation:













20% of a = b      20 a = b.
100



























b% of 20 = b x 20 = 20 a x 1 x 20 = 4 a = 4% of a.
100 100 100 100

7.

In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is of the number of students of 8 years of age which is 48. What is the total number of students in the school?
A. 72 B. 80
C. 120 D. 150
E. 100

View Answer


Answer: Option E


Explanation:


Let the number of students be x. Then,


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













80% of x = 48 + 2 of 48
3












80 x = 80
100

x = 100.


8.

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.
A. 2 : 3 B. 1 : 1
C. 3 : 4 D. 4 : 3

View Answer


Answer: Option D


Explanation:













5% of A + 4% of B = 2  (6% of A + 8% of B)
3


























5  A + 4  B = 2 6  A + 8  B
100 100 3 100 100






















1  A + 1  B = 1  A + 4  B
20 25 25 75























1 1  A =  4 1  B
20 25 75 25















1  A = 1  B
100 75

















A = 100 = 4 .
B 75 3

Required ratio = 4 : 3


9.

A student multiplied a number by 3 instead of 5 .
5 3

What is the percentage error in the calculation?

A. 34% B. 44%
C. 54% D. 64%

View Answer


Answer: Option D


Explanation:


Let the number be x.



















Then, error = 5 x 3 x = 16 x.
3 5 15

















Error% = 16x x 3 x 100 % = 64%.
15 5x

10.

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:
A. 2700 B. 2900
C. 3000 D. 3100

View Answer


Answer: Option A


Explanation:


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


Valid votes polled by other candidate = 45% of 6000
















= 45 x 6000 = 2700.
100

11

Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?
A. 57% B. 60%
C. 65% D. 90%

View Answer


Answer: Option A


Explanation:


Total number of votes polled = (1136 + 7636 + 11628) = 20400.















Required percentage = 11628 x 100 % = 57%.
20400

12.

Two tailors X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
A. Rs. 200 B. Rs. 250
C. Rs. 300 D. None of these

View Answer


Answer: Option B


Explanation:


Let the sum paid to Y per week be Rs. z.


Then, z + 120% of z = 550.













z + 120 z = 550
100












11 z = 550
5













z = 550 x 5   = 250.
11

13.

Gauri went to the stationers and bought things worth Rs. 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
A. Rs. 15 B. Rs. 15.70
C. Rs. 19.70 D. Rs. 20

View Answer


Answer: Option C


Explanation:


Let the amount taxable purchases be Rs. x.












Then, 6% of x = 30
100
















x = 30 x 100 = 5.
100 6

Cost of tax free items = Rs. [25 – (5 + 0.30)] = Rs. 19.70


14.

Rajeev buys good worth Rs. 6650. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax @ 10%. Find the amount he will have to pay for the goods.
A. Rs. 6876.10 B. Rs. 6999.20
C. Rs. 6654 D. Rs. 7000

View Answer


Answer: Option A


Explanation:
















Rebate = 6% of Rs. 6650 = Rs. 6 x 6650 = Rs. 399.
100















Sales tax = 10% of Rs. (6650 – 399) = Rs. 10 x 6251 = Rs. 625.10
100

Final amount = Rs. (6251 + 625.10) = Rs. 6876.10


15.

The population of a town increased from 1,75,000 to 2,62,500 in a decade. The average percent increase of population per year is:
A. 4.37% B. 5%
C. 6% D. 8.75%

View Answer


Answer: Option B


Explanation:


Increase in 10 years = (262500 – 175000) = 87500.















Increase% = 87500 x 100 % = 50%.
175000













Required average = 50 % = 5%.
10

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