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 Percentage Questions

Popular Latest Rated Important Formulae

FACTS  AND  FORMULAE  FOR  PERCENTAGE  QUESTIONS

 

 

I.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% = 20/100 = 1/5;     

48% = 48/100 = 12/25, etc.

To express a/b as a percent : We have, ab=ab×100% .

 

Thus, 14=14×100%=25%

   

 

II. If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is R100+R×100%

If the price of the commodity decreases by R%,then the increase in consumption so as to decrease the expenditure is R100-R×100%

 

 

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

1. Population after n years = P1+R100n

 

2. Population n years ago =  P1+R100n

 

 

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

1. Value of the machine after n years = P1-R100n

 

2. Value of the machine n years ago = P1-R100n

 

 

V. If A is R% more than B, then B is less than A by

R100+R×100%    

If A is R% less than B , then B is more than A by 

R100-R×100%  

Q:

If 1/8 of a pencil is black, 1/2 of the remaining is white and the remaining, 3/2cm is blue. Find the total length of the pencil?

A) 8 cms B) 7 cms
C) 9 cms D) 11 cms
 
Answer & Explanation Answer: A) 8 cms

Explanation:

Let the total length of the pencil = x cms

From the given data,

'x/8' is black

Remaining part = x - x/8 = 7x/8

1/2 of 7x/8 is white

=> 7x/16 is white (Remaining part is 7x/16)

And given that the remaining part is blue and is 3 1/2 cm = 7/2 = 3.5 cm

That remaining part = 7x/16

Therefore,

7x/16 = 7/2

x = 16/2 = 8

Hence, the total length of the pencil = x = 8 cm.

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17 9273
Q:

Read the data given and answer the following questions

 

In a class of 60 students:

 

42 like Maths,

32 like English,

12 like neither Maths nor English

 

How many students like exactly one subject?

A) 16 B) 12
C) 6 D) 22
 
Answer & Explanation Answer: D) 22

Explanation:
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0 9256
Q:

If 35% of a number is 24 less than 50% of that number, then the number is ?

A) 80 B) 160
C) 100 D) 120
 
Answer & Explanation Answer: B) 160

Explanation:

Let the number be n. Then,

50% of n - 35% of n = 24

50/100 n - 35/100 n = 24

n = (24 x 100)/15 = 160.

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8 9084
Q:

A Shepherd had n goats in the year 2000. In 2001 the no.of goats increased by 40% . In 2002 the no. of goats declined to 70%. In 2003 the no. of  goats grew by 30%. In 2004, he sold 10% goats, then he had only 34,398 goats. The percentage increase of the no.of goats in this duration was:

A) 14.66% B) 16.66%
C) 20% D) 33.33%
 
Answer & Explanation Answer: A) 14.66%

Explanation:

There is no need to use the no of goats i.e (34,398). let initially thete be 1000 goats then 

 

  1000 -----> 1400 -----> 980 -----> 1274 ----->1146.6

 

Thus the % increase = (1146.6-1000)/100 x 100= 14.66%

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7 9042
Q:

Read the data given below and answer the questions based on it.

 

In the CBSE Board exams last year, 53% passed in Biology, 61% percent passed in English, 60% in Social studies, 24% in Biology and English, 35% in English and social studies, 27% in Biology and social studies and 5% in none.

 

If the number of students in the class is 200, how many passed in only one subject?

A) 48 B) 46
C) More than 50 D) Less than 40
 
Answer & Explanation Answer: B) 46

Explanation:
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3 9035
Q:

The value of a machine depreciates at the rate of 10% every year. It was purchased 3 years ago. If its present value is Rs. 8,748, its purchase price was ?

A) Rs.14,000 B) Rs.12,000
C) Rs. 12,800 D) Rs. 15,000
 
Answer & Explanation Answer: B) Rs.12,000

Explanation:

We have P = 8748, R = -10 and n = 3
Therefore, the purchase price of the machine
= P1+R100n= 87481-101003
= 8748 x (100/90) x (100/90) x (100/90)
= 12,000.

 

Therefore, the purchase price of the machine was Rs. 12,000.

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7 9007
Q:

In an election only two candidates contested. A candidate secured 70% of the valid votes and won by a majority of 172 votes. Find the total number of valid votes  ?

A) 446 B) 415
C) 404 D) 430
 
Answer & Explanation Answer: D) 430

Explanation:

Let the total number of valid votes be 'V'.

70% of V = 70/100 x V = 7V/10

Number of votes secured by the other candidate = V - 7V/100 = 3V/10

Given, 7V/10 - 3V/10 = 172 => 4V/10 = 172

=> 4V = 1720 => V = 430.

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8 8951
Q:

Solve 30 + (.0825 x 30) + (15% x 30)

A) 24.750 B) 36.975
C) 34.652 D) 26.354
 
Answer & Explanation Answer: B) 36.975

Explanation:

30 + (.0825 x 30) + (15% x 30)

 

Now

=> 0.0825 x 30 = 2.475 -----(1)

=> 15% of 30 = 450/100 = 4.5 -----(2) 

 

Hence, from (1) & (2)

30 + (.0825 x 30) + (15% x 30)

= 30 + 2.475 + 4.5

30 + (.0825 x 30) + (15% x 30) = 36.975.

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19 8852