Question

the price of an article has been reduced by 10% by how much per cent must the new price be increased to retain the original price ??​

Answer 1

Answer:

11.11% must the new price be increased to retain the original price.

Step-by-step explanation:

Given :-

The price of an article has been reduced by 10% .

To find :-

By how much percent must the new price be increased to retain the original price?

Solution :-

Let the original price of an article is 'x'.

The new price of an article is 'y'.

According to question,

The price of an article has been reduced by 10% .

$\bf {i.e. \: x=y-10\% \: \: \text{of} \: \: y}$

$\bf \: x=y-\frac{10}{100}y$

$\bf x=y - 0.1y$

$\bf x=0.9y$

$\bf y= \frac{10}{9} x$

$\bf Total \: increase \: is \frac{10}{9}x-\frac{x}{9}=\frac{x}{9}</p><p>$

Therefore, Percentage increase is

$\bf P= \frac{x}{9} \times \frac{100}{x} </p><p>$

$\bf P= \frac{100}{9} \%$

$\bf P=11.11 \%$

Therefore, 11.11% must the new price be increased to retain the original price.