$A$ man bought apples at the rate of $8$ for $Rs. 34$ and sold them at the rate of $12$ for $Rs. 57$. How many apples should be sold to earn a net profit of $Rs. 45$?

Hundred oranges are bought at the rate of $Rs. 350$ and sold at the rate of $Rs. 48$ per dozen. The percentage of profit or loss is:

Sudeep buys two $CDs$ for $Rs. 380$ and sells one at a loss of $22 \%$ and the other at a gain of $12 \%$. If both the $CDs$ are sold at the same price,then the cost price of the two $CDs$ is (in $Rs.$)

If the cost price of $20$ articles is equal to the selling price of $15$ articles,find the profit percent?

$A$ shopkeeper mixes $20 \, kg$ of rice which cost him $Rs. \, 5$ per $kg$ with $35 \, kg$ of rice which cost him $Rs. \, 7$ per $kg$. Then he sells the mixture at $Rs. \, 6.5$ per $kg$. Find his total profit and percent profit.

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