The printed price of an article is $40 \%$ higher than its cost price. What is the discount rate so that the seller gains a $12 \%$ profit?

$A$ cloth dealer professes to sell cotton at cost price, but uses a meter scale having a length of $80 \, cm$ only and charges for a full meter. Find his gain percent.

$A$ 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.

$A$ man gains $20 \%$ by selling an article for a certain price. If he sells it at double the price,what will be the percentage of profit (in $\%$)?

The marked price of a bed is $Rs. 2400$. The shopkeeper gives successive discounts of $10 \%$ and $X \%$ to the customer. If the customer pays $Rs. 1836$ for the bed,then find the value of $X$ in $\%$.

$A$ shopkeeper sold some articles at $Rs. 35$ per piece and gained $40 \%$. What would be the selling price of each article to earn $60 \%$ profit? (in $Rs.$)