$A$ machine is sold at a profit of $15 \%$. Had it been sold for $Rs\, 540$ more,$24 \%$ would have been gained. Find the cost price.

In these questions,two equations numbered $I$ and $II$ are given. You have to solve both the equations and mark the appropriate option.
$I$. $x^{2} = 16$
$II$. $2y^{2} - 17y + 36 = 0$

$A$ sells an article to $B$ at a profit of $20 \%$ and $B$ sells it to $C$ at a loss of $10 \%$. If $C$ pays $Rs. 540$ for it,at what price did $A$ buy?

$A$ shopkeeper sold decks at $Rs. 166$ each after giving $17\%$ discount on the labelled price. Had he not given the discount,he would have earned a profit of $25\%$ on the cost price. What was the cost price of each deck? (in $Rs.$)

$A$ sells an article to $B$ at a gain of $25 \%$,$B$ sells it to $C$ at a gain of $20 \%$,and $C$ sells it to $D$ at a gain of $10 \%$. If $D$ pays $₹ 330$ for it,how much did it cost $A$? (in $₹$)

$A$ and $B$ started a business by investing $Rs. 3,50,000$ and $Rs. 1,40,000$ respectively. $A$ gets $20\%$ of the yearly profit for managing the business. Thereafter,the profit is divided in the ratio of the capital. If $A$ receives totally $Rs. 38,000$ more than $B$ at the end of a year,then the total profit is (in $Rs.$)