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Successive Percentage Change

Comparing Quantities I - Concepts

Ratio and Percentages

Using OF Operator in Percentages

Express the Fraction as Percentage

Express Decimal as Percentage

Express as Percentage

Percentage Change

Successive Percentage Change

Percentage Increase or Decrease Using Multiplier

Percetage Increase or Decrease

Unitary Method In Percentages

Class - RPF Sub Inspector Subjects

Concept Explanation

Successive Percentage Change

The concept of successive percentage change deals with two or more percentage changes applied to quantity consecutively. In this case, the final change is not the simple addition of the two percentage changes (as the base changes after the first change).

Suppose a number N undergoes a percentage change of x % and then y%, the net change is:

$large New ;number = N times (1 + frac{x}{100}) times (1 + frac{y}{100})$

$large = N times (1 + frac{x}{100}+ frac{y}{100}+frac{xy}{10000})$

$large = N times (1 + frac{1}{100} times (x+y+frac{xy}{100})$

$large = N times (1 + frac{z}{100}) ;where ; z=x+y+frac{xy}{100}$

Here, z is the effective percentage change when a number is changed successively by two percentage changes.

Various cases for Percentage Change:

Both percentage changes are positive: $large x; and; y ;are; positive; and ;then; increase =x+y+frac{xy}{100};%$

One percentage change is positive and the other is negative:

$large x; is; positive ;and; y ;is; negative; then;net; increase$ $large =x-y-frac{xy}{100};%$

Both percentage changes are negative:

$large x; and; y ;are; negative; and ;net; increase =-x-y+frac{xy}{100};%$

Percentage Change involving three changes:

If value of an object/number P is successively changed by x%, y% and then z%, then final value.

percentage-successive-percentage-change

Illustration 1: A’s salary is increased by 10% and then decreased by 10%. The change in salary is

Solution: As firstly salary increases, thus use positive sign and then salary decreases, so use negative sign

Percentage change formula when x is positive and y is negative is given by

$large % ;change=x-y-frac{xy}{100};%$ Here, x = 10, y = 10

$large =10-10-frac{10 ;X ;10}{100};%$

$large =-1%$ As negative sign shows a decrease, hence the final salary is decreased by 1%.

Illustration 2: A number is first increased by 10% and then it is further increased by 20%. The original number is increased altogether by?

Solution : Percentage change formula when both x and y are positive =

$large %;change=x+y+frac{xy}{100};%$

Here, x = 10 and y = 20 Hence net percentage change $large =10 + 20 +frac{ (10 ;X;20)}{100}$

$large =30 +frac{ (200)}{100}$

$large =30 +2$

$large =32%$

As positive sign shows increase, Hence, The original number is increased altogether by 32 %.

Sample Questions

(More Questions for each concept available in Login)

Question : 1

If value of an object P is successively decreased by 10%, 20% and then 30%, then find final value if P = 10?.
A. 5.04	B. 50.40	C. 0.504	D. 5.400
Right Option : A
View Explanation

Question : 2

If value of an object P is successively increased by 10%, 20% and then 30%, then find final value if P =10 ?
A. 17.16	B. 17.17	C. 1716	D. None of these
Right Option : A
View Explanation

Question : 3

The percentage change formula when X is positive and Y is negative ___________________ .
A. $x-y-frac{xy}{100}%$	B. $dpi{100}- x-y+frac{xy}{100}%$	C. $x+y+frac{xy}{100}%$	D. none of these
Right Option : A
View Explanation