$1.$How much water must be added to prepare $1000$ kg of $40\%$ tomato paste from a $75\%$ concentrate?

$2.$How much water must be evaporated for $2500$ kg of $30\%$ sugar liquor to lose half of the water present?

$3.$A plant produces $10,000$ lb$/$day of a $40\%$ tomato juice concentrate from $6\%$ juice. This plant sells its product to another country that reconstitutes the juice, adding water back to a concentration of $12\%,$ which is its commercial grade. How much water is evaporated at the original plant and how much water must be added at the destination plant?