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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:

In an election between two candidates K and L, the number of valid votes received by K exceeds those received by L by 15% of the total number of votes polled. If 20% of the votes polled were invalid and a total of 8720 votes were polled, then how many valid votes did L get ?

A) 3241 B) 2457
C) 2642 D) 2834
 
Answer & Explanation Answer: D) 2834

Explanation:

Let the total number of votes polled in the election be 100k.
Number of valid votes = 100k - 20% (100k) = 80k
Let the number of votes polled in favour of K and L be a and b respectively.
a - b = 15% (100k) => a = b + 15k
=> a + b = b + 15k + b
Now, 2b + 15k = 80k and hence b = 32.5k
It is given that 100k = 8720
32.5k = 32.5k/100k x 8720 = 2834

The number of valid votes polled in favour of L is 2834.

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7 7856
Q:

In a college, number of boys is 75% of number of girls. Difference between boys and girls is 35. On a particular day 20% boys were absent, then find the number of boys those who present?

A) 72 B) 84
C) 93 D) 81
 
Answer & Explanation Answer: B) 84

Explanation:

Ratio of girls and boys = 100% : 75% = 4:3

Difference is 1 unit = 35

So, 3 units = 35 x 3 = 105

If 20% absent, that’s mean 80% present.

So, present boys = 80% of 105 = 80×105100 = 84

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18 7845
Q:

If 25% of three-seventh of 26% of a number is 145.5, what is the number?

A) 4987 B) 5784
C) 5223 D) 4741
 
Answer & Explanation Answer: C) 5223

Explanation:

Given, 

 

25% of three-seventh of 26% of a number is 145.5

 

Let the required number be 'N'

 

i.e, 25100x37x26100xN = 145.5

 

N = 145.5x7x1000075x26

 

=> N = 5223.07

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9 7758
Q:

Lucky started working 2 years ago. Her starting salary was half of Karthik's salary at that time. Each year since then Lucky and Karthik have received a rise of 10% in their respective salary. What percentage (to the nearest percent) of Karthik's current salary is Lucky's current salary ?

A) 75% B) 22.5%
C) 35% D) 50%
 
Answer & Explanation Answer: D) 50%

Explanation:

Let the salary of Karthik 2 years ago be Rs.100
So, Lucky's salary 2 years ago was Rs.50

 

Karthik's present salary has seen two 10 percent increases. So as Lucky's salary.

So, Karthik's salary 1 year ago = 100 + 10% of 100 = 100 + 10 = 110.
Karthik's present salary = 110 + 10% of 110 = 110 + 11 = 121.

 

Lucky's salary 1 year ago = 50 + 10% of 50 = 50 + 5 = 55
Lucky's present salary = 55 + 10% of 55 = 55 + 5.5 = 60.5

 

Lucky's present salary of 60.5 = 50% of Karthik's present salary of 121.

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20 7758
Q:

30% of 500 rupees is?

A) Rs. 180 B) Rs. 150
C) Rs. 120 D) Rs. 240
 
Answer & Explanation Answer: B) Rs. 150

Explanation:

Given 30% of 500

= 30100 x 500= 30 x 5= 150

 

Hence, 30% of Rs. 500 = Rs. 150.

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19 7750
Q:

Ramesh spent Rs. 38460 on the renovation of his home, Rs. 24468 on buying furniture and remaining 28% of the total amount he had as cash with him. What was the total amount ?

A) 87400 B) 92520
C) 88470 D) 90150
 
Answer & Explanation Answer: A) 87400

Explanation:

Let X be the total amount with Ramesh

Given 28% of X = Cash remaining

=> Amount spent = 72% of X = 38460 + 24468 = 62928

=> 72% of X = 62928

=>  X = ?

=> X = 87400

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9 7703
Q:

In order to maximize his gain, a shopping mall owner decides to reduce the price of electronics goods by 20% and as a result of this, the sales of electronics increase by 40%. If, as a result of these changes, he is able to increase his weekly collection by Rs. 1,05,000, find by what value did the gross collection increase per day?

A) Rs. 14400 B) Rs. 14600
C) Rs. 14800 D) Rs. 15000
 
Answer & Explanation Answer: D) Rs. 15000

Explanation:

It won't requires that much solving.

Here given the increase in weekly collection by Rs. 1,05,000

That is this increase denotes for all 7 days.

=> Gross Collection increase per day = Rs. 1,05,0007 = Rs. 15,000

Hence, the gross collection increase per day = Rs. 15,000.

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8 7334
Q:

One-third of the boys and one-half of the girls of a college participated in a sport. If the number of participating students is 300, out of which 100 are boys. What is the total number of students in the college?

A) 500 B) 300
C) 600 D) 700
 
Answer & Explanation Answer: D) 700

Explanation:

Let number of boys in the school = x

Let number of girls in the school = y

Number of students participated in the sports = 300

Out of which boys = 100

but given number of boys participated in sports = x/3

=> x/3 = 100

=> x = 300

Remaining girls = 300 - 100 = 200

=> y/2 = 200

=> y = 400

Therefore, total number of students in the school = x + y = 300 + 400 = 700

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14 7323