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**Percentage**

Percent means for every 100

So, when percent is calculated for any value, it means that we calculate the value for every 100 of the reference value.

percent is denoted by the symbol %. For example, x percent is denoted by x%*x*%=*x/*100

Example : 25%=25/100=1/4- To express
*x/y*as a percent, we have*x/y*=(*x/y*Ã—100)%

Example : 1/4=(1/4Ã—100)%=25%

- If the price of a commodity increases by R%, the reduction in consumption so as not to increase the expenditure = [
*R/*(100+*R*)Ã—100]% - If the price of a commodity decreases by R%, the increase in consumptions o as not to decrease the expenditure = [
*R/*(100âˆ’*R*)Ã—100]% - If the population of a town = P and it increases at the rate of R% per annum, then Population after n years =
*P(*(1+*R)/*100))n - If the population of a town = P and it increases at the rate of R% per annum, then Population before n years =
*P(*(1+*R)/*100))n

Then Value of the machine after n years = *P(*(1-*R)/*100))n

If the present value of a machine = P and it depreciates at the rate of R% per annum,__Solved Examples__

| |

A. None of these | B. A is smaller than B. |

C. Relationship between A and B cannot be determined. | D. If x is smaller than y, then A is greater than B. |

E. A is greater than B. |

**Answer : **Option A

**Explanation :**

A = *xy/*100 â€¦â€¦â€¦â€¦.(Equation 1)

B = *yx/*100.................(Equation 2)

From these equations, it is clear that A = B

| |

A. None of these | B. 10% of a |

C. 4% of a | D. 20% of a |

**Answer : **Option C

**Explanation :**

20% of a = b

=> b = 20a/100

b% of 20 = 20b/100=(20a/100) Ã— 20/100

=(20Ã—20Ã—a)/(100Ã—100)=4a/100 = 4% of a

| |

A. 2 : 1 | B. 1 : 2 |

C. 1 : 1 | D. 4 : 3 |

**Answer : **Option D

**Explanation :**

5% of A + 4% of B = 2/3(6% of A + 8% of B)

5A/100+4B/100=2/3(6A/100+8B/100)

â‡’5A+4B=2/3(6A+8B)

â‡’15A+12B=12A+16B

â‡’3A=4B

â‡’AB=43â‡’A:B=4:3

| |

A. 4% | B. 6% |

C. 5% | D. 50% |

**Answer :** Option C

**Explanation :**

Increase in the population in 10 years = 2,62,500 - 1,75,000 = 87500

% increase in the population in 10 years = (87500/175000)Ã—100=8750/175=50%

Average % increase of population per year = 50%/10=5%

| |

A. 57% | B. 50% |

C. 52% | D. 60% |

**Answer : **Option A

**Explanation :**

Votes received by the winning candidate = 11628

Total votes = 1136 + 7636 + 11628 = 20400

Required percentage = (11628/20400)Ã—100=11628/204=2907/51=969/17=57%

| |

A. 420 | B. 700 |

C. 220 | D. 400 |

**Answer : **Option B

**Explanation :**

He sells 40% of oranges and still there are 420 oranges remaining

=> 60% of oranges = 420

â‡’(60Ã—Total Oranges)/100=420

â‡’Total Oranges/100=7

â‡’ Total Oranges = 7Ã—100=700

| |

A. 499/11 % | B. 45 % |

C. 500/11 % | D. 489/11 % |

**Answer :** Option C

**Explanation :**

Total runs scored = 110

Total runs scored from boundaries and sixes = 3 x 4 + 8 x 6 = 60

Total runs scored by running between the wickets = 110 - 60 = 50

Required % = (50/110)Ã—100=500/11%

| |

A. 2023% | B. 20% |

C. 21% | D. 2223% |

**Answer : **Option B

**Explanation :**

Total numbers = 70

Total numbers in 1 to 70 which has 1 in the unit digit = 7

Total numbers in 1 to 70 which has 9 in the unit digit = 7

Total numbers in 1 to 70 which has 1 or 9 in the unit digit = 7 + 7 = 14

Required percentage = (14/70)Ã—100=140/7=20%

| |

A. 2800 | B. 2700 |

C. 2100 | D. 2500 |

**Answer : **Option B

**Explanation :**

Total number of votes = 7500

Given that 20% of Percentage votes were invalid

=> Valid votes = 80%

Total valid votes = (7500Ã—80)/100

1^{st} candidate got 55% of the total valid votes.

Hence the 2nd candidate should have got 45% of the total valid votes

=> Valid votes that 2nd candidate got = (total valid votes Ã—45)/100

=7500Ã—(80/100)Ã—(45/100)=75Ã—(4/5)Ã—45=75Ã—4Ã—9=300Ã—9=2700

| |

A. 8200 | B. 7500 |

C. 7000 | D. 8000 |

**Answer : **Option D

**Explanation :**

State A and State B had an equal number of candidates appeared.

In state A, 6% candidates got selected from the total appeared candidates

In state B, 7% candidates got selected from the total appeared candidates

But in State B, 80 more candidates got selected than State A

From these, it is clear that 1% of the total appeared candidates in State B = 80

=> total appeared candidates in State B = 80 x 100 = 8000

=> total appeared candidates in State A = total appeared candidates in State B = 8000

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