$A$ man sells an article at $5 \%$ above its cost price. If he had bought it at $5 \%$ less than what he had paid for it and sold it at $Rs. 2$ less,he would have gained $10 \%$. The cost price of the article is (in $Rs.$)

$A$ cycle dealer offers a discount of $10 \%$ and still makes a profit of $26 \%$. What does he pay for a cycle whose marked price is $₹ 840$? (in $₹$)

While selling a watch,a shopkeeper gives a discount of $15 \%$. If he gives a discount of $20 \%$,he earns $Rs. 51$ less as profit. What is the original price of the watch? (in $Rs$)

$A$ trader mixes $26 \text{ kg}$ of rice at $Rs. 20$ per $\text{kg}$ with $30 \text{ kg}$ of rice of another variety at $Rs. 36$ per $\text{kg}$ and sells the mixture at $Rs. 30$ per $\text{kg}$. His profit percent is:

Nutan bought $30$ dozens of oranges for her juice stall in the school fair. She paid $Rs. 8$ per dozen of oranges. She also had to pay $Rs. 500$ as the stall fee to the school authorities. She calculated that each glass of juice would need $3$ oranges. How much should she charge per glass of juice so as to make $20 \%$ profit in $Rs$?

In these questions,two equations numbered $I$ and $II$ are given. You have to solve both the equations and mark the appropriate option.
$I.$ $2x^2 + 19x + 45 = 0$
$II.$ $2y^2 + 11y + 12 = 0$