Question

Raman sells an article at a loss of 10%. If he had sold it for 30 more, he would have gained 5%.find
the cost price of the article​.

Answer 1

GIVEN :-

• Raman sells an article at a loss of 10%.
• If he had sold it for 30 more , he would have gained 5%.

TO FIND :-

• Cost price of article.

SOLUTION :-

Let the cost price of article be 'x'.

Raman sells the article at 10% loss.

Selling price = x - 10% of x

$\sf \: selling \: price = x - \dfrac{10x}{100} \\ \\ \sf \: selling \: price = \dfrac{100x - 10x}{100} \\ \\ \sf \: selling \: price = \dfrac{9 \cancel0x}{10 \cancel0} \\ \\ \underline{ \sf \: selling \: price = \dfrac{9x}{10} }$

Also, if he had sold it for 30 more , he would have gained 5%.

Selling price + 30 = x + 5% of x

$\\ \implies\sf \: \dfrac{9x}{10} + 30 = x + \dfrac{5}{100}(x) \\ \\ \implies\sf \: \dfrac{9x}{10} - x - \dfrac{5x}{100} = - 30 \\ \\ \implies \sf \: \dfrac{9x(10) - x(100) - 5x(1)}{100} = - 30 \\ \\ \implies \sf \: \dfrac{90x - 100x - 5x}{100} = - 30 \\ \\ \implies \sf \: - 6x = - 30 \times 100 \\ \\ \implies \sf \: - 6x = - 3000 \\ \\ \implies\sf \: x = \dfrac{ - 3000}{ - 6} \\ \\ \implies \overline{\underline{\boxed{\sf \: x = 500}}}$

Hence , cost of article is 500.