A man buys a cycle for $Rs$ $1400$ and sells it at a loss of $15 \% .$ What is the selling price of the cycle? (in $Rs.$)

A trader buys $500\, kg$ of cotton for $Rs.\, 9,000.10 \%$ of this cotton is spoiled due to rain. At what rate ($Rs./ kg$) should he sell the rest to earn $10 \%$ profit?

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?

By selling $90$ pens for $Rs.\, 80$ a man loses $20 \%$. What should be the selling price (in $Rs.$) of $90$ pens for $20\%$ profit?

The profit earned by selling an article for $Rs.\, 900$ is double the loss incurred when the same article is sold for $Rs.$ $450 .$ At what price should the article be sold to make $25 \%$ profit in $Rs.$?

The marked price of an article is $Rs.\, 5000.$ But due to a special festive offer a certain per cent of discount is declared. Mr. $X$ availed this opportunity and bought the article at reduced price. He then sold it at $Rs.\, 5000$ and thereby made a profit of $11 \frac{1}{9} \%$. The percentage of discount allowed was