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Study Notes on Percentage with Quiz

Percentage: A fraction whose denominator is 100 is called percentage. and The numerator of the fraction is called the rate percent.
1. To express x% as a fraction:
We have, x% = x/100

      Thus, 30% = 30/100 =3/10

2. To express fraction as percentage,
we have ,

 a/b =  {a/b x100}%
                           

3. If A is R% more than B, then B is less than A by

  {(R/(100+R)x100}% 

4. If A is R% less than B, then B is more than A by

   {(R/(100-R)x100}% 

5. If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is:

  {(R/(100+R)x100}% 

6. If the price of a commodity decreases by R%, then the increase in consumption so as not to decrease the expenditure is:

  {(R/(100-R)x100}% 

7. Let the population of a town be P now and suppose it increases at the rate of R% per annum, then

   1. Population after n years = P(1+R/100)^n

   2.Population before n years =P/(1 + R/100)^n

8. Let the present value of a machine be P. Suppose it depreciates at the rate of R% per annum.

   1.Value of the machine after n years= P(1-R/100)^n
                                                        
   2.Value of the machine n years ago=P/(1-R/100)^n 
                         
9. For two successive changes of x% and y%, net change

   {x + y +xy/100}%


1. A shopkeeper announces successive discounts of 10% and 20%. Find the equivalent percent discount.
A.  27%
B.  28%
C.  29%
D.  30%

2. In a college, 40% of the students were allotted group A, 75% of the remaining were given group B and the remaining 12 students were given group C. Then the number of students who applied for the groups is:
A.  80
B.  92
C.  100
D.  60

3.Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are:
A. 39, 30
B. 41, 32
C. 42, 33
D.43, 34

4. In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State?
A. 8200
B. 7500
C. 7000
D. 8000

5. The price of a car is Rs. 3,25,000. It was insured to 85% of its price. The car was damaged completely in an accident and the insurance company paid 90% of the insurance. What was the difference between the price of the car and the amount received ?
A. Rs. 76,375
B. Rs. 34,000
C. Rs. 82,150
D. Rs. 70,000

6. Gauri went to the stationers and bought things worth Rs. 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
A. Rs. 15
B. Rs. 15.70
C. Rs. 19.70
D. Rs. 20

7. In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is  of the number of students of 8 years of age which is 48. What is the total number of students in the school?
A. 72
B. 80
C. 120
D. 100

8. A's salary is 30% higher than B's salary. The percent that B's salary is less than A's salary is:
A.  25%
B.  30%
C.  23 1/13%
D.  20%

9. If the price of sugar is increased by 25%, by how much percent must a householder reduce his consumption of sugar so as not to increase his expenditure on sugar?
A.  35%
B.  30%
C.  25%
D.  20%

10. In a class of 40 students and 8 teachers, each student got sweets that are 20% of the total number of students and each teacher got sweets that are 25% of the total number of students. How many sweets were there?
A.  420
B.  400
C.  320
D.  360

Answer and Solution :
1(B)Explanation
For two successive changes of x% and y%, net change =
     {x + y +xy/100}%
  = {-10-20+(-10)(-20)/100}%
  =(-30 + 2) %
  = - 28%

2(A)Explanation
Let the number of students be 100.
Number of students allotted to group A = 40
Number of students allotted to group B = 75% of 60 = 45
Thus, Balance number of students allotted to group C = 100 - 40 - 45 = 5
Number of actual students = 100/15 * 12 = 80

 3(C)Explanation:
Let their marks be (x + 9) and x.
Then, x + 9 = 56/100(x + 9 + x)
 =>25(x + 9) = 14(2x + 9)
 =>3x = 99
 =>x =33
 So, their marks are 42 and 33.

4(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

5(A)Explanation :
Price of the car = Rs.3,25,000
Car insured to 85% of its price
=>Insured price=325000×85/100
Insurance company paid 90% of the insurance
Amount paid by Insurance company =Insured price×90/100
=325000×85/100×90/100=325×85×9=Rs.248625
Difference between the price of the car and the amount received
= Rs.325000 - Rs.248625 = Rs.76375

6(C)Explanation:
Let the amount taxable purchases be Rs. x.
Then, 6% of x = 30/100
=> x = (30/100 x 100/6) = 5
so  Cost of tax free items = Rs. [25 - (5 + 0.30)] = Rs. 19.70

7(D)Explanation:
Let the number of students be x. Then,
Number of students above 8 years of age = (100 - 20)% of x = 80% of x.
so  80% of x = 48 + 2/3 of 48
=> 80/100 x = 80
=> x = 100.

8(C)Explanation:
Let B's salary be Rs. 100
Then , A's salary = Rs.130
Required percentage = 30/100 * 100 = 23 1/13%

9(D) Explanation:
If the price of a commdity increases by R% , then the reduction in consumption so as not to increase the expenditure is :
   {(R/(100+R)x100}%
Thus, percent reduction in consumption =  {(25/(100+25)x100}%
 = 20 %

 10(B)Explanation :
Number of students in the class = 40
Sweets received by 40 students = 40 * (20% of 40) = 320
Number of teachers in the class = 8
Sweets received by 8 teacher  = 8 * (25% of 40) = 80
Total number of sweets = 320 + 80 = 400

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