$A$ sells an article to $B$ at $15 \%$ profit. $B$ sells it to $C$ at $10 \%$ loss. If $C$ pays $₹ 517.50$ for it,then $A$ purchased it at:

$A$ trader allows a trade discount of $20 \%$ and a cash discount of $6 \frac{1}{4} \%$ on the marked price of the goods and gets a net gain of $20 \%$ of the cost. By how much above the cost should the goods be marked for the sale? (in $\%$)

$A$ person sells taperecorders at $Rs. 1134$ each after giving a discount of $19 \%$ on the marked price. Had he not given the discount,he would have earned a profit of $40 \%$ on the cost price. The cost price of each taperecorder is (in $Rs.$)

$A$ shopkeeper mixes $26 \, kg$ of wheat which costs $Rs. 20$ per $kg$ with $30 \, kg$ of wheat which costs $Rs. 36$ per $kg$ and sells the mixture at $Rs. 30$ per $kg$. Find the profit percent. (in $\%$)

Raheem sells a machine for $RS. 48$ lakh at a loss. Had he sold it for $RS. 60$ lakh,his gain would have been $5$ times the former loss. Find the cost price of the machine in lakh $Rs.$?

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