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?

$A$ pen was sold for a certain sum and there was a loss of $20 \%$. Had it been sold for $Rs. 12$ more,there would have been a gain of $30 \%$. What would be the profit percentage if the pen was sold for $Rs. 4.80$ more than the original selling price?

$A$ fruit seller bought $240$ bananas at the rate of $Rs. 48$ per dozen. He sells half of them at the rate of $Rs. 5$ per banana. $\frac{1}{6}$ of the remaining bananas are found to be rotten. At what price per banana must he sell the remaining bananas to get a profit of $25\%$ on his entire investment?

$A$ shopkeeper sells a badminton racket,whose marked price is $Rs. 30$,at a discount of $15\%$ and gives a shuttlecock costing $Rs. 1.50$ free with each racket. Even then,he makes a profit of $20\%$. His cost price per racket is (in $Rs$):

Nutan bought a watch with $24 \%$ discount. If she pays $Rs. 779$ for that watch,then what is the marked price of the watch in $Rs.$?

$A$ and $B$ jointly made a profit of $Rs. 1650$ and they decided to share it such that $\frac{1}{3}$ of $A$'s profit is equal to $\frac{2}{5}$ of $B$'s profit. Then the profit of $B$ is (in $Rs.$)