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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 the given two numbers are respectively 7% and 28% of a third number, then what percentage is the first of the second ?

A) 24% B) 29%
C) 34% D) 25%
 
Answer & Explanation Answer: D) 25%

Explanation:

Here, k = 7 and l = 28
Therefore, first number = klx100 % of second number = 7/28 x 100% of second number = 25% of second number.

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12 10312
Q:

An exhibition was conducted for 4 weeks. The number of tickets sold in 2nd workweek was increased by 20% and increased by 16% in the 3rd workweek but decreased by 20% in the 4th workweek. Find the number of tickets sold in the beginning, if 1392 tickets were sold in the last week ?

A) 1124 B) 1420
C) 1345 D) 1250
 
Answer & Explanation Answer: D) 1250

Explanation:

Let initially 'X' ticket has been sold.
So now in 2nd week 20% increases, so
=> X x 120/100
In 3rd week 16% increases, so
=> X x (120/100) x (116/100)
In 4th week 20% decrease, so
=> X x (120/100) x (116/100) x (80/100) = 1392
X = 1250.

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6 10296
Q:

Two numbers are respectively 40% and 30% more than a third number. The second number expressed in terms of percentage of the first is ?

A) 92.8% B) 84.23%
C) 87.14% D) 94.1%
 
Answer & Explanation Answer: A) 92.8%

Explanation:

Here, x = 40 and y = 30;
Therefore second number
= [[100+y100+x] x 100 ]% of first number
= [[100+y100+x] x 100 ]% of first number
Second number = 92.8% of the first number.

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12 10238
Q:

5% people of a village in India died by dengue, 15% of the remainder left the village on account of fear. If now the population is reduced to 3553, how much was it in the beginning ?

A) 4400 B) 3100
C) 2800 D) 5600
 
Answer & Explanation Answer: A) 4400

Explanation:

Let 'P' be the original population at the beginning

P x (95/100) x (85/100) = 3553

P = 4400.

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9 10145
Q:

One-quarter of one-seventh of a land is sold for Rs. 30,000. What is the value of an four fifteenth of land ?

A) Rs.1,92,000 B) Rs.2,24,000
C) Rs.1,26,000 D) Rs.3,42,000
 
Answer & Explanation Answer: B) Rs.2,24,000

Explanation:

One-quarter of one-seventh = 1/4 x 1/7
= 1/28
Now, 1/28 of a land costs = Rs. 30,000
Thus, 8/35 of the land will cost = 30,000 x 28 x 4/15
= Rs. 2,24,000.

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15 9977
Q:

If the price of a commodity is decreased by 20% and its consumption is increased by 10%, what will be the increase or decrease in the expenditure on the commodity?

A) increase 12% B) decrease 12%
C) increase 16% D) decrease 16%
 
Answer & Explanation Answer: B) decrease 12%

Explanation:

Given the price of a commodity is decreased by  p = 20%

And its consumption is increased by q = 10%

Now, required increase or decrease in the expenditure on the commodity can be 

p + q + pq/100 = -20 + 10 - 200/100 = -10 - 2 = -12%.

 

Hence, decrease in the expenditure = 12%

 

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8 9807
Q:

If x is 90% of Y, what percent of x is y?

Answer

x = 90% of y = \inline \frac{9}{10}y


 


\inline \therefore \frac{x}{y}=\frac{9}{10}\Rightarrow \frac{y}{x}=\frac{10}{9} 


=> y = 1.1% of x.

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Subject: Percentage

24 9640
Q:

A house owner wants to get his house painted. He is told that this would require 45 kg of paint allowing 6% wasting. And if the paint is available in 4 kg tins only, the number of tins required for painting the house is ?

A) 12 B) 13
C) 11 D) 10
 
Answer & Explanation Answer: A) 12

Explanation:

Given 45 kg for painting 

And 6% 0f 45 for wasting => 6x45/100 = 2.7 kg

Now total paint required = 45+2.7 = 47.7 kgs

But tins are available in only 4kgs

Then, no. of tins req = 47.7/4 = 11.4 => 12 tins

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14 9602