**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