If a shopkeeper sells $25$ articles at $Rs. 45$ per article after giving $10 \%$ discount and earns $50 \%$ profit. If the discount is not given,what is the profit percentage gained?

$A$ shopkeeper sold an item at $10 \%$ loss after giving a discount equal to half the marked price. The cost price of the item is ......... of the marked price.

Kamya purchased an item for $Rs.\, 46,000$ and sold it at a loss of $12\%$. With that amount,she purchased another item which she sold at a gain of $12\%$. What was her overall gain or loss?

$A$ trader sold an article at a gain of $20 \%$. Had he purchased it for $40 \%$ more and sold for $Rs. 24$ less,he would have incurred a loss of $20 \%$. What is the cost price (in $Rs.$) of the article?

In these questions,two equations numbered $I$ and $II$ are given. You have to solve both the equations and mark the appropriate option.
$I.$ $2x^2 - 11x + 15 = 0$
$II.$ $2y^2 - 11y + 14 = 0$

Oil equal to $20 \%$ of the weight of groundnut is extracted in a mill. The matter left after extraction is sold as cattle feed at the rate of $Rs. 12.5$ per $kg$. The groundnuts are bought at $Rs. 20$ per $kg$ and the processing cost is $Rs. 5$ per $kg$. At what price ($Rs.$ per $kg$) should the oil be sold to earn $20 \%$ profit on total costs (Total cost $=$ cost of groundnuts and processing costs)?