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All questions of Percentage And Its Applications for Judiciary Exams Exam

If the radius of circle is increased by 110% its area is increased by
  • a)
    110      
  • b)
    301         
  • c)
    341
  • d)
    501    
Correct answer is option 'C'. Can you explain this answer?

Kavya Saxena answered
Option ( c) 341 is correct. 
Explanation:- 
{Let the initial radius of circle = 10 cm
Then, it's area = π r^ 2 
=  π (10) ^2 
=  100 π cm square. 
Given, (radius is  increased by 110%) 
New radius = ( 100+110) % of 10 cm
=> 210% of 10 cm
{ 210 /100 * 10} cm
=> 21 cm
Therefore, area of circle of radius (21) cm
=> π (21) ^2 
=>  441 π cm square. 
Increase in area=  ( 441 π - 100 π ) cm square. 
=> 341 cm square. }

A man’s wages were decreased by 50%. Again the reduced wages were increased by 50%. He has a loss of:
  • a)
    0%
  • b)
    0.25%
  • c)
    2.5%
  • d)
    25%
Correct answer is option 'D'. Can you explain this answer?

Let 100 be the wages of man if it decreases by 50%, his wages become 100-(50%of 100) = 100-50 =50 Now his wages is 50 when it is increases by 50% then angain his salery become 50+(50%of50) = 50+25 = 75 He has loss of 100-75 = 25 In % = (25×100)/100 = 25% Thus he has loss of 25%. Hence option (d) is correct.

A number when increased by 37 ½% gives 33. The number is:
  • a)
    22
  • b)
    24
  • c)
    25
  • d)
    27
Correct answer is option 'B'. Can you explain this answer?

Kavya Sharma answered
x increased by 37 1/2% ( of x) gives 33, or
x + (37 1/2 % * x) = 33
x + (37.5%x) = 33
1x + (.375x) = 33
1.375x = 33
Divide both sides by 1.375
x = 24

In an examination, Summit got 30% marks and failed by 15 marks. In the same examination, Rohit got 40% marks, which is 35 marks more than the pass marks. Then what is the total marks in the examination?
  • a)
    500
  • b)
    250
  • c)
    600
  • d)
    450
Correct answer is option 'A'. Can you explain this answer?

Shanaya Sharma answered
Let the total marks be x.
Sumit got = 30% of x
= 0.3x
Passing marks = 0.3x+15

Rohit got = 40% of x
= 0.4x
Passing marks = 0.4x - 35

Equating both passing marks , we get
0.3x+15 = 0.4x - 35
50 = 0.1x
x = 500

Total marks = 500 , i.e. , option a) 500

In an examination, Summit got 30% marks and failed by 15 marks. In the same examination, Rohit got 40% marks, which is 35 marks more than the pass marks. Then what is the total marks in the examination?
  • a)
    500
  • b)
    250
  • c)
    600
  • d)
    450
Correct answer is option 'A'. Can you explain this answer?

Shanaya Sharma answered
Let the total marks be x.
Sumit got = 30% of x
= 0.3x
Passing marks = 0.3x+15

Rohit got = 40% of x
= 0.4x
Passing marks = 0.4x - 35

Equating both passing marks , we get
0.3x+15 = 0.4x - 35
50 = 0.1x
x = 500

Total marks = 500 , i.e. , option a) 500

Rajesh is 40% older thanNeeraj. Find how much % is Neeraj younger than Rajesh.
  • a)
      
  • b)
  • c)
    25%  
  • d)
    None
  • e)
    All of the above
Correct answer is option 'A'. Can you explain this answer?

Crafty Classes answered
Given:
  • Rajesh is 40% older than Neeraj.
We need to find out how much percentage younger Neeraj is compared to Rajesh.
Step 1: Let Neeraj's age be N.
  • Since Rajesh is 40% older, Rajesh's age will be:
    Rajesh’s age = N + 40% of N = N + 0.4N = 1.4N
Step 2: Find the percentage by which Neeraj is younger than Rajesh.
  • The difference in age between Rajesh and Neeraj is:
    Difference in age = 1.4N − N = 0.4N
  • Now, to find how much younger Neeraj is as a percentage of Rajesh's age, we use the formula:
Substituting the values:

Neeraj is 28.57% younger than Rajesh, which matches the fraction 
Thus, the correct answer is Option A: 

A student who gets 36% of marks, fails by 32 marks. Another candidate who gets 45% marks gets 40 marks more than are necessary for passing. Find the maximum marks.
  • a)
    1600  
  • b)
    600
  • c)
    400  
  • d)
    None
  • e)
    All of the above
Correct answer is option 'B'. Can you explain this answer?

Aarav Sharma answered
Given:

- A student who gets 36% of marks, fails by 32 marks.
- Another candidate who gets 45% marks gets 40 marks more than are necessary for passing.

To find:

- Maximum marks

Solution:

Let the maximum marks be x.

From the given data,

- The first student gets 36% marks and fails by 32 marks. So,
- Marks obtained by the first student = 36% of x
- Marks required to pass = (100% - 36%) of x = 64% of x
- According to the question, the first student fails by 32 marks. So,
- 36% of x - 64% of x = 32
- -28% of x = 32
- x = 32/(-28%) = 114.28 ≈ 114 (rounded off to the nearest integer)

- The second student gets 45% marks and gets 40 marks more than are necessary for passing. So,
- Marks obtained by the second student = 45% of x
- Marks required to pass = (100% - 45%) of x = 55% of x
- According to the question, the second student gets 40 marks more than are necessary for passing. So,
- 45% of x - 55% of x = 40
- -10% of x = 40
- x = 40/(-10%) = 400

Therefore, the maximum marks are 400.

Hence, option B is the correct answer.

On decreasing the price of TV set by 30%, its sale is increased by 20%. What is the effect on the revenue received by the shopkeeper?
  • a)
    10% increase
  • b)
    10% decrease
  • c)
    16% increase
  • d)
    16% decrease
Correct answer is option 'D'. Can you explain this answer?

Kavya Sharma answered
Lets take the orignal price as 100. Then on decreasing the price by 30% we get= 70. Now the sale is increased by 20%=84 (20% of 70 or 20/100*70= 14 now 70+14=84) So we can say that Cp=100 and Sp=84 Thats loss as cp is bigger. Loss=16 Loss%=16/100*100 =16% 

Petrol prices are reduced by 20%. Find by how much percent a vehicle owner must increase his consumption of petrol so as not to decrease his expenditure of petrol.
  • a)
    20%  
  • b)
    25%
  • c)
    42%  
  • d)
    None
  • e)
    All of the above
Correct answer is option 'B'. Can you explain this answer?

Given:
  • Petrol prices are reduced by 20%.
  • We need to find by how much percentage a vehicle owner must increase his consumption so that his expenditure does not decrease.
Step 1: Understanding the situation.
If the price of petrol has decreased by 20%, it is now 80% of what it was before. To keep the expenditure the same, the vehicle owner must increase his consumption so that the total expenditure remains constant.
Step 2: Formula to calculate the percentage increase in consumption:
The formula to calculate the percentage increase required is:

In this case, the reduction in price is 20%, or 0.20.
Step 3: Substituting the values into the formula:

The vehicle owner must increase his consumption by 25% to maintain the same expenditure on petrol.

The price of milk has risen by 75%. Find by how much percent a house holder must reduce his consumption so as not to increase his expenditure.
  • a)
      
  • b)
  • c)
      
  • d)
    None
  • e)
    All of the above
Correct answer is option 'C'. Can you explain this answer?

Crafty Classes answered
Given:
  • The price of milk has increased by 75%.
  • We need to find by what percentage a householder must reduce his consumption so that his expenditure does not increase.
Step 1: Understanding the situation.
If the price of milk has risen by 75%, the price is now 1.75 times what it was before. To keep the expenditure the same, the householder must reduce his consumption in such a way that the total expenditure remains constant.
Step 2: Formula to calculate the percentage reduction in consumption:
The formula to calculate the percentage reduction required is:

In this case, the increase in price is 75%, or 0.75.
Step 3: Substituting the values into the formula:

Percentage reduction = 0.4286 × 100 = 42.86%
Step 4: Simplifying:
The reduction in consumption should be approximately
The householder must reduce his consumption by
Therefore, the correct answer is Option C.

At an election a candidate secures 40% votes and is defeated by the other candidate by a majority of 2020 votes. Find the total number of votes polled.
  • a)
    9900  
  • b)
    10000
  • c)
    10100 
  • d)
    None
  • e)
    All of the above
Correct answer is option 'C'. Can you explain this answer?

Sajal Bdw answered
A candidate who was defeated got 40% of vote therefore it can be concluded that it the candidate who won the election got 60% of vote
So now let's consider total number of votes are x So according to question we have
60x÷100-40x÷100=2020
or,20x÷100=2020
or,x=10100 Therefore the answer

A reduction of 20% in the price of rice enables a man to buy 10 kg more rice for Rs. 1600. Find the reduced price of rice per kg.
  • a)
    Rs. 25  
  • b)
    Rs. 12
  • c)
    Rs. 32 
  • d)
    None
  • e)
    All of the above
Correct answer is option 'C'. Can you explain this answer?

Sajal Bdw answered
Let the original price of rice = Rs. x/kg
New price = Rs 4x/5 kg
According to question,
[1600/(4x/5)] - (1600/x) = 10
=>(8000/4x) - (1600/x) = 10
=>40x = 1600 {By solving above equation}
=>x = 40
Hence the original price of rice is 40 rupees per kg.
for the reduced price equal to=(4/5)×40
=32
therefore the new price of rice is 32 rupees per kg
HENCE OPTION C IS THE ANSWER

A student has to secure 35% marks to pass. He gets 650 marks and fails by 50 marks. Find the maximum marks.
  • a)
    1000  
  • b)
    1500
  • c)
    2000  
  • d)
    None
  • e)
    All of the above
Correct answer is option 'C'. Can you explain this answer?

Aarav Sharma answered
Problem Solving Strategy:
Let the maximum marks be x.
According to the given question,
35% of x = 650 + 50
= 700
Hence, we can find x by using the formula:
35/100 * x = 700
x = 2000

Solution:
Therefore, the maximum marks are 2000. Hence, the correct answer is option (c).

In an examination, 42% students failed in Hindi and 52% failed in English. If 17% failed in both the subjects, the percentage of those who passed in both the subject is
  • a)
    23%
  • b)
    27%
  • c)
    34%
  • d)
    40%
Correct answer is option 'A'. Can you explain this answer?

Aarav Sharma answered
Solution:

Given,
Percentage of students failed in Hindi = 42%
Percentage of students failed in English = 52%
Percentage of students failed in both the subjects = 17%

Let's assume the total number of students appeared for the examination be 100.

Number of students failed in Hindi = 42% of 100 = 42
Number of students failed in English = 52% of 100 = 52
Number of students failed in both subjects = 17% of 100 = 17

Now, we need to find the percentage of students who passed in both subjects.

Number of students who failed in at least one subject = Number of students failed in Hindi + Number of students failed in English - Number of students failed in both subjects
= 42 + 52 - 17 = 77

Number of students who passed in both subjects = Total number of students - Number of students who failed in at least one subject
= 100 - 77 = 23

Percentage of students who passed in both subjects = (Number of students who passed in both subjects / Total number of students) * 100%
= (23/100) * 100%
= 23%

Therefore, the percentage of students who passed in both subjects is 23%, which is option A.

  • a)
    1414  
  • b)
    5600
  • c)
    700  
  • d)
    None
  • e)
    All of the above
Correct answer is option 'D'. Can you explain this answer?

Crafty Classes answered
Given:

This is a percentage problem, where we need to calculate 
Step 1: Convert the mixed fraction to an improper fraction
Step 2: Convert the percentage to a decimal
To convert a percentage to a decimal, divide by 100:
Step 3: Multiply by 1600
Now, calculate:
0.875 × 1600 = 1400
None of the given options match the correct answer of 1400.
Therefore, the correct option is: D: None

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