Given:
An item was sold at a loss of 20%.
If the item is sol for Rs. 50 more then, the profit would have been 5%.
To find:
The cost price of the item.
Solution:
Let x be the cost price of the item.
The item was sold at a loss of 20%. Then selling selling price is:
[tex]S.P.=x-\dfrac{20}{100}x[/tex]
[tex]S.P.=x-0.2x[/tex]
[tex]S.P.=0.8x[/tex]
If a the item is sold for 5% profit, then the selling price is:
[tex]S.P.=x+\dfrac{5}{100}x[/tex]
[tex]S.P.=x+0.05x[/tex]
[tex]S.P.=1.05x[/tex]
It is given that, if the item is sol for Rs. 50 more then, the profit would have been 5%. So,
[tex]0.8x+50=1.05x[/tex]
[tex]50=1.05x-0.8x[/tex]
[tex]50=0.25x[/tex]
Divide both sides by 0.25.
[tex]\dfrac{50}{0.25}=x[/tex]
[tex]200=x[/tex]
Therefore, the cost price of the item is Rs. 200.
