Question

the difference between increasing a number by 5% and decreasing it by 5% is 20 what is the number​

Answer 1

Answer:

Let the number be x

It is increased by 5% ⇒ x + \frac{x}{20} = \frac{21x}{20}x+

20

x

=

20

21x

Also, it is decreased by 5% ⇒ x - \frac{x}{20} = \frac{19x}{20}x−

20

x

=

20

19x

The difference between these two is 20

\frac{21x}{20} - \frac{19x}{20} = 20

20

21x

−

20

19x

=20

⇒ 2x = 400

⇒ x = 200

The number is 200

Answer 2

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❥︎ Given :

The difference between increasing a number by 5% and decreasing it by 5% is 20

❥︎ To find :

The number

❥︎ Solution :

Let the number be x.

➜ Increasing the number by 5% :

→ $x + 5 \% \; of \: x$

→ $x + \frac {5}{100} × x$

→ $x + \frac {x}{20}$

→ $\frac {20x + x} {20}$

→ $= \frac {21x}{20}$

➜ Decreasing the number by 5% :

→ $x - 5 \% \:of \: x$

→ $x - \frac {5}{100} × x$

→ $x - \frac {x} {20}$

→ $\frac {20x - x} {20}$

→ $= \frac {19x}{20}$

➜ The difference between increasing a number by 5% and decreasing it by 5% is 20 :

→ $\frac {21x}{20} - \frac {19x}{20} = 20$

→ $\frac {2x}{20} = 20$

→ $2x = 20 × 20$

→ $2x = 400$

→ $x = \frac {400}{2}$

$\implies \textbf {Hence, the number is 200.}$

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