Question

1. A man sold an article for Rs. 6800 and incurred a loss. Had he sold the article for Rs. 7600, his gain
would have been equal to half of the amount of the loss that he incurred. At what price should he sell
the article to have 20 % profit?​

Answer 1

Step-by-step explanation:

6800 subtracted the xvalue

Answer 2

$\begin{lgathered} \red{\bf{Given}}\begin{cases} \sf \: sp1(when \: loss) = 6800 \\ \sf \: sp2(when \: profit) = 7600 \\ \sf gain = \frac{loss}{2} \end{cases}\end{lgathered}$

Let CP of Article be Rs.X ...

now, we know that,

$\green{\boxed{ \bf \: gain = sp - cp}} \\ \\ \blue{\boxed{ \bf \: loss = cp - sp}}$

So,

$\sf \: Gain = (7600 - x) \: \\ \sf \: loss = (x - 6800)$

Now, it is given that, gain is Half of loss ,,

so,

$\blue{(7600 - x) = \frac{(x - 6800)}{2}} \\ \\ \red\longrightarrow \: 2(7600 - x) = (x - 6800) \\ \\ \red\longrightarrow \: \orange{15200 - 2x = x - 6800} \\ \\ \red\longrightarrow \: 3x = 15200 + 6800 \\ \\ \red\longrightarrow \: 3x = 22000 \\ \\ \red\longrightarrow \: \pink{\large\boxed{\boxed{\bold{x = \frac{22000}{3} }}}}$

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Now, Question is what Price he sell to gain 20% ...

we know that,,

$\boxed{\sf \: sp = \dfrac{cp \times (100 + p \%)}{100} } \\ \\ \green{\bf \: putting \: value \: we \: get} \\ \\ \red{\boxed\implies} \: sp = \frac{220 \cancel{00} \times \cancel{120}}{ \cancel3 \times \cancel{ 100}} \\ \\ \red{\boxed\implies} \: \red{\large\boxed{\boxed{\bold{Rs.8800}}}}$

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Hence, he must sell the article at Rs.8800 to gain 20% ..

$\large\underline\textbf{Hope it Helps You.}$

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