Percentage

### Important Points to Remember:

1. If the price of a commodity increases by R%, the reduction in consumption so as not to increase the expenditure=

2. If the price of a commodity decreases by R%, the increase in consumption so as not to decrease the expenditure=

3. If the present value of a machine=P & it depricates at the rate of R% per annum, Then value of the machine after n years=

4. If the present value of a machine=P & it depricates at the rate of R% per annum, Then value of the machine before n years=

5. If A's income is more than B's income by x%, then B's income is less than A's income by=

6. If A's income is less than B's income by x%, then B's income is more than A's income by=

7. If any quantity is first increased by x% then reduced by x%, then there is always a loss of=

8. If the Population of a town=P & it increases at the rate of R% per annum, then Population after n years=

9. If the Population of a town=P & it increases at the rate of R% per annum, then Population before n years=

10. If the population of any town is P and the rate of percentage change per annum for three years are r1%, r2% & r3% respectively, then population of town after three years will be

11. If there are two students who score r1% and r2% marks respectively and first fails by x marks and second one passed by y marks, then maximum marks of the examination is=

12. If in an examination r1% students failed in one subject and r2% students failed in another subject and r3% students failed in both subjects, then percentage of total failed students is=

Percentage of total passed students is=

13. In an examination there are A boys and B girls. r1% boys out of A boys and r2% girls out of B girls passed in the examination, then percentage of passed students will be=

14. If the price of any commodity is first increased by r1% and then again increased by r2%, then total percentage of increment=

15. If the price of any commodity is first increased by r1% and then again reduced by r2%, the total percentage of increment or decrement will be=

16. If any person expend r1% of his salary on first item and r2% of remaining on another item and in the last he has Rs x, then the salary of that person will be=

17. If the price of any commodity is reduced by r% due to this any person can buy A Kg more for Rs x, then the original value of commodity is=

## Questions Asked from this Chapter:

### Question Type 1: Based on the Basic Concept of Percentage

**Example:**

30% of x is 72. The vakue of x is?

a) 216

b) 240

c) 480

d) 640

**Solution:**

### Question Type 2: If "X" is less/more than "Y" by "M%" then "Y" exceed/less than "X" by?

**Example:**

If A's salary is 25% higher than B's salary, how much percent is B's salary lower than A's?

a) 16%

b) 20%

c) 25%

d) 33.33%

**Solution:**

### Question Type 3: Based on Income, Expenditure, Salary and Wages

**Example:**

### If A's income is 20% more than that of B, By how much percent is B's income less than that of A?

a) 16*(4/5)

b) 16*(1/3)

c) 16*(2/3)

d) 16*(2/7)

**Solution:**

### Question Type 4: Based on Ratio

**Example:**

### Two numbers are respectively 20% and 50% more than a third number. The ratio of two numbers is:

a) 2:5

b) 3:5

c) 4:5

d) 6:7

**Solution:**

### Question Type 5: Based on Number System

**Example:**

### When 60 is subtracted from 60% of a number, the result is 60. The number is:

a) 120

b) 150

c) 180

d) 200

**Solution:**

**Example:**

The sum of number of boys and girls in a school is 150. If the number of boys is x, the number of girls becomes x% of total number of students. The number of boys is:

a) 90

b) 50

c) 40

d) 60

**Solution:**

### Question Type 6: Based on Allegation and Mixture

**Example:**

### How much water must be added to 100ml of 80% solution of boric acid to reduce it to a 50% solution?

a) 30 ml

b) 40 ml

c) 50 ml

d) 60 ml

**Solution:**

### Question Type 7: Based on Fractions

**Example:**

The numerator of a fraction is increased by 20% and denominator decreased by 20%. The value of fraction becomes 4/5. The original fraction is:

a) 2/3

b) 8/15

c) 7/11

d) 4/5

**Solution:**

### Question Type 8: If the Price of useful thing rises/reduces by x%. By how much percent should the Consumption of that thing be reduced/rised so that the expenditure does not change.

**Example:**

The price of a sugar goes up by 20%. If the house wants the expenses of sugar to remain same, she should reduces the consumption by:

a) 15*(1/5)

b) 16*(2/3)

c) 20%

d) 25%

**Solution:**

### Question Type 9: Question Based on Examination

**Example:**

### In an examination, who gets 20% of the maximum marks fails by 5 marks. Another student who scores 30% of the maximum marks gets 20 marks more than the passing marks. The necessary percenatge required for passing is:

a) 32%

b) 23%

c) 22%

d) 20%

**Solution:**

**Example:**

A student has to obtain 33% of total marks to pass. He got 25% of total marks and failed by 40 marks. The number of total marks is:

a) 800

b) 300

c) 500

d) 1000

**Solution:**

### Question Type 10: Based on Passed/Failed students in an Examination

**Example:**

In a examination, 52% students failed in Hindi and 42% in English. If 17% failed in both subjects, what percentage of students passed in both the subjects?

a) 38%

b) 33%

c) 23%

d) 18%

**Solution:**

### Question Type 11: If some thing(Price, Salary, length etc.) first increase/decrease then decrease/increase i.e based on x+y+xy/100

**Example:**

A number is increased by 10% and then decreased by 10%. Finally the number.

a) does not change

b) decrease by 1%

c) increase by 1%

d) increases by 0.1%

**Solution:**

**Example:**

The price of an article was increased by 10% and then again by 20%. If the last increased price is Rs 33, the original price was:

a) Rs 30

b) Rs 27.50

c) Rs 26.50

d) Rs 25

**Solution:**

### Question Type 12: Based on Voters in an Election

**Example:**

Two candidates contested in a election. One got 60% of the votes and won by 1600 votes. What is the number of votes polled?

a) 9000

b) 8000

c) 10000

d) 7500

**Solution:**

### Question Type 13: Based on Rate of Increase or Decrease

**Example:**

The value of a machine depricate by 5% every year. If its present value is Rs 2,00,000, its value after 2 years will be:

a) Rs 1,80,500

b) Rs 1,99,000

c) Rs 1,80,000

d) Rs 2,10,000

**Solution:**

### Question Type 14: After increasing/decreasing the price of any useful item by x%, a customer can buy "y" Kg less or more than things for "Rs z" Find the Reduced/Increased Price?

**Example:**

The reduction of 20% in the price of an apple enables a man to buy 10 apples more for Rs 54. The reduced price of apples per dozen is:

a) Rs 4.32

b) Rs 12.96

c) Rs 10.80

d) Rs 14.40

**Solution:**