Question

a number is increases by 20 then decreases by 20
find the net increases or decreases in the number

Answer 1

Answer:

Step-by-step explanation:

$\bf\underline{Given:-}$

A number is increases by 20% then decreases by 20%.

$\bf\underline{To \: Find:-}$

Increases or decreases in the number

$\bf\underline{Solution:-}$

Let the Given Number be 100.

$\bf\underline{According \: to \: the \: Question}$

Increase in the number = 20%

Increased Number $\sf= 100-96 = 4$

$\sf\implies \frac{20}{100}\times100=20$

The number decreased by 20%

Decrease in the number = $\sf \frac{20}{100}\times120=12\times2=24$

New number = $\sf 120-24 = 96$

Now, net decrease = $\sf100-96 = 4$

Net % Decrease = $\sf\frac{Net \: Decrease}{Original \: Number}\times100$

Net % Decrease = $\sf\frac{4}{100}\times100$

$\underline{\bold{Net \: \% \: Decrease = 4 \: \%.}}$

Answer 2

Question:

If a number is increased by 20% and then decreased by 20% , then find the net percentage increase or decrease in the number.

Solution:

Let the initial number be x.

Now,

When the initial number is increased by 20% ,then the new number will be;

=> x + 20% of x

=> x + (20/100)x

=> x + x/5

=> (5x + x)/5

=> 6x/5

Now;

When the new number is decreased by 20% ,then the final number will be;

=> 6x/5 - 20% of (6x/5)

=> 6x/5 - (20/100)(6x/5)

=> 6x/5 - (1/5)(6x/5)

=> (6x/5)(1 - 1/5)

=> (6x/5){(5 - 1)/5}

=> (6x/5)(4/5)

=> 24x/25

Note:

The net percentage change is given as ;

( Final - Initial )( 100/Initial ) %

Thus,

The percentage change in the number will be given as ;

(Final no. - initial no.)(100/initial no.) %

ie ;

=> (24x/25 - x)(100/x) %

=> {(24x - 25x)/25}(100/x) %

=> (- x/25)(100/x) %

=> - 100/25 %

=> - 4%

{ Here, the negative sign shows that , there is net decrease in the number}

Hence,

There will be net percentage decrease of 4% in the number.