Question

an item was sold at loss of 20%. had it been sold for rs3000 more then the profit would have been 10%. What is the cost price of the item

Answer 1

Answer:

Let cost price of item = x.

Sold at loss of 20% = [(100 - 20)/100] * x = 0.8 x.

Profit would have been 10% = [(100 + 10)/100] * x = 1.1 x

It been sold for 3000.

=> 0.8 x + 3000 = 1.1 x

=> 0.8 x - 1.1 x = -3000

=> -0.3 * x = -3000

=> x = 10000

Therefore, cost price of item = 10,000.

Hope this helps!

Answer 2

AnswEr :

Let's assume that the CP be Rs. x

$\bold{Given} \begin{cases}\sf{Cost \: Price (CP)=Rs. x} \\ \sf{Loss=20\%}\\ \sf{Selling \: Price(SP)=?}\end{cases}$

• Formula for the SP when it's Loss :

$\longrightarrow \sf SP = CP \times (100 - Loss)\%$

$\longrightarrow \sf SP = x \times (100 - 20)\%$

$\longrightarrow \sf SP = x \times 80\%$

$\longrightarrow \sf SP = x \times \cancel\dfrac{80}{100}$

$\longrightarrow \sf SP = x \times \dfrac{4}{5}$

$\longrightarrow \sf SP = \dfrac{4x}{5}$

$\rule{300}{1}$

• Given Situation Now :

If it had been sold for Rs.3000 more than SP then the profit would have been 10%.

$\bold{Given} \begin{cases}\sf{Cost \: Price (CP)=Rs. x} \\ \sf{Profit=10\%}\\ \sf{Selling \: Price(SP)=\dfrac{4x}{5} + 3000 }\end{cases}$

• Formula for the SP when it's Profit :

$\Longrightarrow \sf SP =CP \times (100 + Profit)\%$

$\Longrightarrow \sf \dfrac{4x}{5} + 3000 = x \times (100 + 10)\%$

$\Longrightarrow \sf \dfrac{4x + 15000}{5} = x \times 110\%$

$\Longrightarrow \sf \dfrac{4x + 15000}{5} = x \times \dfrac{110}{100}$

$\Longrightarrow \sf \dfrac{4x + 15000}{\cancel5} = \dfrac{110x}{\cancel{100}}$

$\Longrightarrow \sf \dfrac{4x + 15000}{1} = \dfrac{110x}{20}$

$\Longrightarrow \sf 20(4x + 15000)=110x$

$\Longrightarrow \sf 80x + 300000=110x$

$\Longrightarrow \sf 300000=110x - 80x$

$\Longrightarrow \sf 300000=30x$

$\Longrightarrow \sf \cancel\dfrac{300000}{30}=x$

$\Longrightarrow \boxed{\sf x =Rs. \: 10000}$

⠀

∴ Hence, Cost Price of Item is Rs. 10,000.