By selling cloth at $Rs. 9$ per meter,a shopkeeper loses $10 \%$. Find the rate at which it should be sold so as to earn a profit of $15 \%$ (in $Rs.$).

An article is marked for sale at $Rs. 504$. The shopkeeper gives a discount of $5\%$ on the marked price and still earns a profit of $20\%$. What is the cost price of the article? (in $Rs.$)

Ram sells an article to Girish at a gain of $20 \%$,Girish sells it to Sanjay at a gain of $10 \%$,and Sanjay sells it to Aditya at a gain of $12 \frac{1}{2} \%$. If Aditya pays $Rs. 59.40$,what did it cost Ram in $Rs.$?

Ajit calculates his profit percentage on the selling price,whereas Rohit calculates his on the cost price. They find that the difference between their profits is $Rs. 100$. If the selling price for both of them is the same and both of them get a $25\%$ profit,find their selling price (in $Rs.$).

By selling a fan for $Rs. 1900$,a man has a loss of $5 \%$. At what price (in $Rs.$) should he sell the fan to gain $20 \% ?$

Raheem sells a machine for $RS. 48$ lakh at a loss. Had he sold it for $RS. 60$ lakh,his gain would have been $5$ times the former loss. Find the cost price of the machine in lakh $Rs.$?