Tricks to solve Percentage Problems - PDF

Percentage is a fraction whose denominator is always 100. x percentage is represented by x%.

To express x% as a fraction : 

We know

x% = ^x/100

Thus 10% = ¹⁰/100 (means 10 parts out of 100 parts)

= ¹/10 (means 1 part out of 10 parts)

To express x/y as a percentage :

We know that ^x/y  = (^x/y× 100 )

Thus ¹/4 = ( ¹/4 ×100 )% = 25%

and 0.8 = ( ⁸/10 ×100 )% = 80%

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

[ ^R/_(100+R)×100 ] %

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

[ ^R/_(100-R)×100 ] %

Result on Population : 

Let the population of a town be P now and suppose increases the rate of R% per annum, then :

1. Population after n years = P ( 1+ ^R/100 )ⁿ 
2. Population  n years ago = ^P /_{( 1+ ^R/100 )ⁿ} 

Result on Depreciation : 

Let the present value of a machine be P. Suppose depreciates at the rate of R% per annum Then :
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} 

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

[ ^R/_(100+R)×100 ]%

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

[ ^R/_(100-R)×100 ]%

• Net % change = x + y + xy/100

Some Observation

#1 

If 20% candidate failed in an exam then observations are

• 80% represent passed in exam
• 100% represent total appeared in exam
• (80%-20%) = 60% represent difference between passed and failed candidate in exam

#2

 If a number is increased by 25% then observations are 

• 100% represent the old number
• 125% represent the new number.

#3

 Remember that Base in the given sentence (Question) is always 100%

Eg. Income of Ram is increased by 20% 

In this sentence 

100% - represent the income of Ram

20% - represent increment

120% - represent new income of Ram.

Remember it :

1 = 100%

1/2 = 50%

1/3 = 33 1/3%

1/4 = 25%

1/5 = 20%

1/6 = 16²/3%

1/7 = 14²/7%

1/8 = 12¹/2%

1/9 = 11¹/3%

1/10 = 10%

1/11 = 9¹/11%

1/10 = 8¹/3%

1/13% = 7⁹/13%

25% = 1/4

6.25% = 1/16

125% = 5/4

150% = 3/2

200% = 2

350% = 7/2

Examples

#1 

Q. If the difference between 62% of a number and 3/5th of that number is 36. what is the number ?

Sol:

Let the number be x.

Then x × 62% - x × ³/5 = 36

x ×62% -x V 60% = 36 (60% = 3/5)

x ×2% = 36

x ×²/100 =36

x = ^36 ×100/2 = 1800

#2

Q. 40% of Ram's income Rs. 1200 Then Find 

1. 75% of Ram's income ?
2. 1/4 part of Ram's income ?
3. 1/3 part of Ram's income ?

Sol :

(1)

40% = 1200 Rs.

75% = 1200/40 ×75 = 2250 Rs.

Trick : 1200 / 40  × 75 = Rs. 2250/-

(2)

40% of income = Rs. 1200

Then 1/4 part (i.e. 25% ) of Ram's

income = 1200/40 ×25 

= Rs. 750/- Ans

(3)

40% of Ram's income

= Rs. 1200

i.e. 2/5 part of Ram's income

= Rs. 1200

Then total income of Ram 

= Rs. 1200 ×5/2

1/3 part of Ram's income

= Rs. 1200  × ⁵/2  × ¹/3 

= Rs. 1000 Ans.

Trick :

¹²⁰⁰/_2/5  × 1/3

= ¹²⁰⁰/2 × ⁵/3 = 1000

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