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 $20 \% ?$

Nitin bought some oranges at $Rs. 40$ a dozen and an equal number at $Rs. 30$ a dozen. He sold them at $Rs. 45$ a dozen and made a profit of $Rs. 480$. The total number of dozens of oranges he bought was:

$A$ shopkeeper mixes $20 \, kg$ of rice which cost him $Rs. \, 5$ per $kg$ with $35 \, kg$ of rice which cost him $Rs. \, 7$ per $kg$. Then he sells the mixture at $Rs. \, 6.5$ per $kg$. Find his total profit and percent profit.

$Mr.$ $A$ sold goods to $Mr.$ $B$ at a $10\%$ discount on the printed rate. The discounted value is $Rs. 1242$. If a $15\%$ profit is earned on the purchase rate by selling the goods at the printed rate,what is the purchase rate? (in $Rs.$)

$A$ fair price shopkeeper takes $10 \%$ profit on his goods. He lost $20 \%$ of his goods due to theft. What is his loss percentage (in $\%$)?

Half of $100$ items were sold at a profit of $20 \%$ and the remaining were sold at a profit of $40 \%$. If all the items were sold at a profit of $25 \%$,the total profit would have been $Rs. 100$ less than the previous profit. What was the cost price (in $Rs.$) of each item?