Question

An item was sold at a loss of 20% . Had been sold for rupees 50 more than the profit would have been 5% . What is the CP of article?​

Answer 1

GIVEN :-

• An item was sold at a loss of 20%.
• If it had been sold for 50 more , profit would have been 5%.

TO FIND :-

• Cost Price (CP) of the item.

SOLUTION :-

Let the CP of the item be 'x'.

It was sold at a loss of 20%.

Selling Price = x - [20% of x]

$\sf \: selling \: price = x - \dfrac{20}{100} (x) \\ \\ \sf \: selling \: price = \frac{100x - 20x}{100} \\ \\ \sf \: selling \: price = \frac{8 \cancel0x}{10 \cancel0} \\ \\ \underline{ \sf \: selling \: price = \frac{8x}{10} }$

Also , if it had been sold for 50 more , profit would be 5%.

Selling price + 50 = x + [5% of x]

$\\ \implies \sf \: \dfrac{8x}{10} + 50 = x + \dfrac{5}{100} (x) \\ \\ \implies \sf \: \dfrac{8x}{10} - x - \dfrac{5x}{100} = - 50 \\ \\ \implies\sf \: \dfrac{8x(10) - x(100) - 5x(1)}{100} = - 50 \\ \\ \implies\sf \: \dfrac{80x - 100x - 5x}{100} = - 50 \\ \\ \implies \sf \: \dfrac{ - 25x}{100} = - 50 \\ \\ \implies\sf \: - 25x = - 5000 \\ \\ \implies \sf \: x = \cancel\dfrac{- 5000}{ - 25} \\ \\ \implies \boxed{\sf \: x = 200}$

Hence , CP of item is 200.

Answer 2

Answer:

CP = 50 rupees

P = 12℅

SP = CP(100+P℅)/100

50(100+12)/100

50×112/100

56