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:

When a discount of Rs. 42 is allowed on the marked price of an article, the new reduced price becomes 86% of the original price. Find the marked price.

A) Rs.250 B) Rs.300
C) Rs.350 D) Rs.400
 
Answer & Explanation Answer: B) Rs.300

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Q:

A shopkeeper marks his goods 40% above the cost price and allows a discount of 25% on it. His gain % is

A) 5% B) 10%
C) 15% D) 20%
 
Answer & Explanation Answer: A) 5%

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Q:

In a motor of 120 machine parts, 5% parts were defective. In another motor of 80 machine parts, 10% parts were defective. For the two motors considered together, the percentage of defective machine parts were

A) 7 B) 6.5
C) 7.5 D) 8
 
Answer & Explanation Answer: A) 7

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Q:

When a number is increased by 21, it becomes 114% of itself. What is the number?

A) 150 B) 252
C) 315 D) 189
 
Answer & Explanation Answer: A) 150

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Q:

A merchant marked cloth at Rs. 50/metre . He offers 2 successive discounts of 15% and 20%. The net price/metre is

A) Rs. 32.50 B) Rs. 42.50
C) Rs. 34.00 D) Rs. 40.00
 
Answer & Explanation Answer: C) Rs. 34.00

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Q:

A's income is 25% more than B's income. B's income is what percent of A's income?

A) 80 B) 75
C) 50 D) 25
 
Answer & Explanation Answer: A) 80

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Q:

If the price of sugar is decreased by 18%, then a person can buy 16.2 kg sugar more for Rs 4500. What will be the new price (in Rs) of sugar per kg?

A) 40 B) 60
C) 45 D) 50
 
Answer & Explanation Answer: D) 50

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Q:

When a number is increased by 18, it becomes 106% of itself. What is the number?

A) 300 B) 216
C) 270 D) 162
 
Answer & Explanation Answer: A) 300

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