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

In these questions, two equations mabered $I$ and $II$ are given. You have to solve both the equations and mark the appropriate option.

$I.$ $3 x^{2}-13 x+12=0$

$II.$ $2 y^{2}-15 y+28=0$

If $11$ Mango are bought for $Rs.\, 10$ and sold at $10$ for $Rs.\, 11 .$ What was Gain or Loss $\% ?$

A men 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 $Rs.$ $45 ?$

A man purchased some eggs at $3$ for $Rs.\, 5$ and sold them at $5$ for $Rs.\, 12 .$ Thus, he gained $Rs.\, 143$ in all. The number of eggs he bought 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 $Rs?$