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:

Three strategies P, Q and R have been initiated for cost cutting in a company producing respectively 20%, 30% and 10% savings. Assuming that they operate independently, what is the net saving achieved ?

A) 49.6% B) 50.4%
C) 33.67% D) 66.66%
 
Answer & Explanation Answer: A) 49.6%

Explanation:

As these three strategies P, Q and R are independent so these will cut cost one after the other.
If initial cost is Rs 100, then
20% cost is cut after initializing strategy P, then cost will remain 80% = 80
further 30% cost is cut after strategy Q, then cost will remain 70% of 80 = 56
further 10% cost is cut after strategy R, then cost will remain 90% of 56 = 50.4

Thus final cost remains 50.4 % of the original cost. Hence net saving is 100 - 50.4 = 49.6 %.

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Q:

Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 10 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B ?

A) 76% B) 72%
C) 80% D) 82%
 
Answer & Explanation Answer: C) 80%

Explanation:

circumference of A = 2πr = 8 => so r = 4π
volume = π×4π2×10 = 160π
circumference of B = 2πr   = 10 => so r = 5π
volume = π×5π2×8 =  200π
so ratio of capacities = 160/200 = 0.8
so capacity of A will be 80% of the capacity of B.

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Q:

A man reduces his travelling time by a fraction of 2/5, as a result the distance covered by the man is increased by 20%, find the percentage increase in the speed of the man ? 

A) 77% B) 88%
C) 100% D) 99%
 
Answer & Explanation Answer: C) 100%

Explanation:

IBPS RRB Clerk Level Quiz : Quantitative Aptitude | 15 -09 - 17

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Q:

What percent is 120 of 85 ?

A) 133.33 % B) 141.17 %
C) 145.54 % D) 139.29 %
 
Answer & Explanation Answer: B) 141.17 %

Explanation:

Px85100=120

 

=> p = 12000/85 = 141.17 %

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Q:

One hour is what percent of a day?

A) 5.6% B) 4.16%
C) 3.35% D) 6.7%
 
Answer & Explanation Answer: B) 4.16%

Explanation:

A day has 24 hrs

=> If 24 hrs - 100

Then 1 hr = ?

100/24 = 4.16%

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Q:

The price of a car is increased by 25%, by how much percent, must the new price of this car be decreased to restore its original price ?

A) 20% B) 24%
C) 21% D) 25%
 
Answer & Explanation Answer: A) 20%

Explanation:

Suppose that the original price of the car = Rs. x 

Then new price of the car

=> (x) + (×25/100) Rs. 5x/

To restore the original price, the new price must be decreased by

5x/− x/4

So required percentage =(x/4)/(5x/4) × 100%

= 20%

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Q:

82.5% of 2360?

A) 1960 B) 1954
C) 1947 D) 1931
 
Answer & Explanation Answer: C) 1947

Explanation:

Given 82.5% of 2360

 82.5100 x 2360 = 0.825 x 2360 = 1947

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Q:

What is 15 of 80 with simple method and examples?

A) 12.5% B) 18.75%
C) 16.55% D) 17.80%
 
Answer & Explanation Answer: B) 18.75%

Explanation:

Given that to find 15 of 80

=> What % of 80 is 15

Let it be 'p'

=> p% of 80 = 15

=> p x 80100 = 15p = 15 x 10080p = 150080 = 18.75

 

Therefore, 15 is 18.75% of 80 => 18.75% of 80 = 15

 

Example::

Now, in the similar way we can find 15% of 80 =?

=> 15x80/100 = p

=> p = 4 x 3 = 12

 

Therefore, 15% of 80 = 12

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