Question

If an article is sold for Rs 178 at a loss of 11%. What shall be its selling price in order to earn a profit of 11%.​

Answer 1

First scenario, we sold for 178Rs at a loss of 11%, we can write this in mathematical form as

$x- \frac{11}{100}x = 178$

$→ \frac{100-11}{10}x = 178$

On further solving we get

$→ \frac{89}{100}x = 178$

$→ x = 200$

So the Actual price of the article is 200Rs.

Second scenario, to find the selling price if we sell it at 11% profit, we can write this in mathematical form as

Assuming our selling price as ${a}$

$x+\frac{11}{100}x = a. . . . . . . . .(2).$

$→ \frac{100+11x}{100}= a$

$→\frac{111x}{100} = a. . . . . . . . .(3).$

Now to calculate the value of ${a}$

we have to put the value of ${x=200}$ in equation (3) we get our equation as

$→\frac{111(200)}{100}=a$

Which on solving gives ${a=200}$

Conclusion, actual value of article is Rs 200 after selling it on 11% loss it becomes Rs 178 and on selling it on 11% profit it becomes Rs 222.

Answer 2

First scenario, we sold for ₹178 at the loss of 11%, we can write this in mathematical way

$x - \frac{11}{100}x = 178$

$\frac{100 - 11}{100} x = 178$

Simplifying further we get,

$\frac{89}{100} x = 178$

$x = \frac{100}{89} \times 178$

$x = 200$

So the initial price of the article is ₹200

Second scenario, we need to find the selling price if we sell it at 11% profit, we can write this in mathematical form as

Assuming our selling price as a

$x + \frac{11}{100} x = a$

$\frac{100 + 11}{100} x = a$

$\frac{111}{100} x = a$

$\frac{111}{100} \times 200 = a$

$a = 222$

$so \: the \: cost \: of \: article \: is \: \boxed{ \green{₹222}}$