Question

a number is first increase 25% and then decreased by 25% .find the net increase or decrease percent.

Answer 1

Successive percentage change:

If No. is increased, sign for %change= +
If it is decreased, sign for % change = -

If a No. is changed (Increased/Decreased) successively by x% and y%, then net %change is given by

net %change
= [x + y + (xy/100) ]%
It represents increase or decrease in value according as the sign is +ve or -ve

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SOLUTION:
Here
x = +25
y = -25
x*y= -625
net %change
= [+25 - 25 +(-625/100)]%
= -(625/100)%
= -(25/4)%
= -6.25%

Since the sign is -ve, the no. decreases by 6.25%

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Proof for the %change formula:
let given no. be N
If it is increased by x%,then it becomes
N+ x% of N
= Nx+(Nx/100)
= N(x+100)/100

If it is further increased by y%, then it becomes
N(x+100)/100+[(y/100)* N(x+100)/100]
= N(x+100)(y+100)/(100)²
Net change= {[N(x+100)(y+100)]/(100)²} -N
=[N(100x+ 100y+xy)]/(100)²
% change= N(x + y + (xy/100))*(1/100)*(100/N)

°•° %change= (x+ y+ (xy/100))%

;)
Hope it helps

Answer 2

Answer:

The net decrease percent is 6.25%.

Step-by-step explanation:

A number is first increase by 25% and then decrease by 25%.

This is a problem of percentage.

For solving this problem first we should know concept of percentage.

a% of b means $\frac{a}{100} \times b = \frac{ab}{100}$

For example,

20% of 300 $= \frac{20}{100} \times 300 = 20 \times 3 = 60$

Here given that a number first increase by 25%.

Let the number be x.

After increasing 25%,the number will be

$x \times \frac{100 + 25}{100} = x \times \frac{125}{100} = x \times \frac{5}{4} = \frac{5x}{4}$

Then again in decrease by 25%.

So now number is

$\frac{5x}{4} \times \frac{100 - 25}{100} = \frac{5x}{4} \times \frac{75}{100} = \frac{ \frac{5}{4} \times 75 }{100} x = \frac{93.75}{100} x$

Therefore now number decrease by

$(100 - 93.75)\% = 6.25\%$