$A$ dairyman pays $Rs. 6.40$ per litre of milk. He adds water and sells the mixture at $Rs. 8$ per litre,thereby making $37.5\%$ profit. The proportion of water to milk received by the customers is

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?

Kunal bought a suitcase with $15 \%$ discount on the labelled price. He sold the suitcase for $Rs. 2880$ with $20 \%$ profit on the labelled price. At what price did he buy the suitcase? (in $Rs.$)

Raman sells a machine for $Rs. 39$ lakh at a loss. Had he sold it for $Rs. 49$ lakh,his gain would have been three times the loss. What is the cost price of the machine? (in $Rs. \text{ lakh}$)

The selling price of a chair is $Rs. 1386$. If the loss percentage is $23\%$,what is the cost price (in $Rs.$) of the chair?

$A$ 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?