Question

24.At what profit percentage must
an article he sold so that by sell-
ing at half that price, there may
be a loss of 30%?​

Answer 1

Answer:-

Let the SP of the article be x and it's CP be y.

Given:

On selling the article of half of the original SP , a loss of 30% is occured.

Here,

• SP = x/2
• Loss% = 30%
• CP = y.

We know that,

SP = (100 - loss% / 100) * CP

So,

⟶ x/2 = (100 - 30 / 100) * y

⟶ x/2 = 70y/100

⟶ (x/2) * (100/70) = y

⟶ 5x/7 = y -- equation (1)

Now,

We have to find the profit% occured on selling the article for the original SP.

We know,

SP = (100 + profit% / 100) * CP

So,

⟶ x = (100 + profit% / 100) * y

Substitute the value of y from equation (1).

⟶ x = ( 100 + profit% / 100) * 5x/7

⟶ x * (7/5x) * 100 = 100 + profit%

⟶ 140 = 100 + profit%

⟶ 140 - 100 = profit%

⟶ 40% = Profit %

∴ The article must be sold at a profit of 40%.

Answer 2

$\huge \mathfrak \red{Answer:-}$

$\sf \: Let \: \: SP \: \: = \: \: 100 \: , \: New \: \: SP \: \: = 50$

$\sf \: CP = \frac{50}{0.7}$

$\sf \: P = 100 - \frac{500}{7} = \frac{200}{7}$

$\sf \: P \per = \: \frac{ \frac{200}{7} }{ \frac{500}{7} } = 40 \per \:$