Question

a number is increased by 15% and decreased by 10% find the net percentage increase or decrease​

Answer 1

AnswEr :

• Let the Number be 100.

• According to the Question Now :

$\longrightarrow \rm Number\times (100 + Inc.)\%\times (100 - Dec.)\%$

$\longrightarrow \rm 100\times (100 + 15)\%\times (100 - 10)\%$

$\longrightarrow \rm 100\times 115\%\times90\%$

$\longrightarrow \displaystyle \rm \cancel{100}\times \frac{115}{\cancel{100}} \times \frac{90}{100}$

$\longrightarrow\rm115 \times 0.9$

$\longrightarrow \rm103.5$

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• Net% Change(Increase/Decease) will be :

$\leadsto \displaystyle\sf Change\% = \frac{Change}{Old\:Number} \times 100$

$\leadsto \displaystyle\sf Change\% = \frac{New\:Number - Old\:Number}{Old\:Number} \times 100$

$\leadsto \displaystyle\sf Change\% = \frac{103.5 - 100}{100} \times 100$

$\leadsto \displaystyle\sf Change\% = \frac{3.5}{ \cancel{100}} \times \cancel{100}$

$\leadsto\boxed{\sf Change\% =3.5 \%}$

⠀

∴ Net Change Percentage will be 3.5%

Answer 2

Answer:

$\large \bold\red{Net\:\%\:Increase=3.5\%}$

Step-by-step explanation:

Let,

The given number is 100.

Now,

According to Question,

It's increased by 15%.

Therefore,

The new number after increment is,

$= 100 + \frac{15}{100} \times 100 \\ \\ = 100 + 15 \\ \\ = 115$

Now,

It's said that,

The number formed is deceased by 10%.

Therefore,

We get,

The new number is,

$= 115 - \frac{10}{100} \times 115 \\ \\ = 115 - 11.5 \\ \\ = 103.5$

Now,

• Original Number = 100
• New number = 103.5

Clearly,

The new number is greater than the original number,

Therefore,

There is increase.

And,

Increase = 103.5 - 100 = 3.5

Therefore,

Increase % is given by,

$= (\frac{increase}{original \: number} \times 100) \% \\ \\ = ( \frac{3.5}{100} \times 100)\% \\ \\ = \large \bold{3.5\%}$

Hence,

There is net increase of 3.5% in the number.