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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:

The Shopkeeper increased the price of a product by 25% so that customer finds it difficult to purchase the required amount. But somehow the customer managed to purchase only 70% of the required amount. What is the net difference  in the expenditure on that product?

A) 10% more B) 5% more
C) 12.5% more D) 17.5% more
 
Answer & Explanation Answer: C) 12.5% more

Explanation:

    Quantity  X  Rate =  Price

 

         1  x  1  =  1

 

       0.7 x 1.25 = 0.875

 

      Decrease in price = (1-0.875) x 100 = 12.5%

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18 12069
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 12030
Q:

At an examination in which maximum marks are 500. P got 10% less than Q, Q got 25% more than R and R got 20% less than S. If P got 360 marks what percentage of marks was obtained by S ?

A) 77 B) 74
C) 80 D) 83
 
Answer & Explanation Answer: C) 80

Explanation:

Let marks obtained by S = M

R's marks = 0.80M

Q's marks = 1.25 (0.80M)

P's marks = (0.90) (1.25) (0.80M)

= 0.9M

But 0.9M = 360

M = ?

M = 400

Hence % of marks obtained by S

= 400/500 x 100 = 80%.

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11 11687
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 11523
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 11262
Q:

A farmer divides his herd of k cows among his 4 sons, so that one son gets one half of the herd, the second gets one-fourth, the third gets one-fifth and the fourth gets 9 cows. Then k is equal to ?

A) 160 B) 120
C) 140 D) 180
 
Answer & Explanation Answer: D) 180

Explanation:

Given total number of cows = k
Now, 1st son share = k/2
2nd son share = k/4
3rd son share = k/5
4th son share = 9

(k) + (k/4) + (k/5) + 9 = k
=> k - (19k/20) = 9
=> (20k-19k)/20 = 9
=> k = 180.

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17 10862
Q:

In measuring the sides of a rectangle, one side is taken 20% in excess and the other 10% in deficit. Find the error per cent in area calculated from the measurement ?

A) 8% excess B) 9% deficit
C) 12% excess D) 11% deficit
 
Answer & Explanation Answer: A) 8% excess

Explanation:

Since  Area of Rectangle = side1 x side2
Therefore, error% in area
= x + y + xy100 %
= [20 - 10 + ( -10 x 20)/100]% or 8%
i.e. 8% excess.

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7 10737
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 10619