# Percentage

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:

a) 16*(4/5)
b) 16*(1/3)
c) 16*(2/3)
d) 16*(2/7)
Solution:

a) 2:5
b) 3:5
c) 4:5
d) 6:7

### 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:

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:

### 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

### 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

### 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: