Question

If a shopkeeper sells an item at a 15% profit instead of a 15% loss, then he earns Rs. 850 more then find the purchase price.

Answer 1

❏ Question:-

@ If a shopkeeper sells an item at a 15% profit instead of a 15% loss, then he earns Rs. 850 more then find the purchase price.

❏ Solution:-

✏ Given:-

• loss % is = 15 %
• profit% is = 15%
• earning amount = 850 Rs .

✏ To Find:-

LET, the purchase price is = X Rs.

Now , the selling price of the item if it's sold at 15 % profit is,

$\sf\longrightarrow S_{profit} = X\,+X\times15\%$

$\sf\longrightarrow S_{profit} = X\,+X\times\dfrac{15}{100}$

$\sf\longrightarrow S_{profit} = \dfrac{115\,X}{100}$

Now , the selling price of the item if it's sold at 15 % loss is,

$\sf\longrightarrow S_{loss} = X\,-\,X\times15\%$

$\sf\longrightarrow S_{loss} = X\,-\,X\times\dfrac{15}{100}$

$\sf\longrightarrow S_{loss} = \dfrac{85\,X}{100}$

• The shopkeeper sold that item at a 15% profit instead of a 15% loss, then he earns Rs. 850 more

$\sf\implies \dfrac{115\,X}{100}-\dfrac{85\,X}{100}=850$

$\sf\implies \dfrac{115\,X-85\,X}{100}=850$

$\sf\implies \dfrac{30\,X}{100}=850$

$\sf\implies 30\,X=85000$

$\sf\implies X=\dfrac{85000}{30}$

$\sf\implies X=\dfrac{85000}{30}$

$\sf\implies \large{\boxed{ X=\red{2833.33}\: Rs}}$

∴ The purchase price is = 2833.33 Rs.