If m and n are positive integers, what is the value of?

(1) mn = 12

(2) is in lowest terms and is in lowest terms.

A Shopkeeper wants to make th profit on her cost by diluting, with water, concentrate to specification and sells it at the rate at which she bought a litre of the concentrate. find the water:concentrate ratio in the diluted solution.

There are two alloys, A and B, of copper and zinc. The ratio (by weight) of copper and zinc in alloy A is 8 : 1 and that in alloy B is 2 : 7. It is found that, if alloy A and alloy B are mixed in a certain ratio, the weights of copper and zinc in the resultant alloy are also in that ratio. What is that ratio?

A milkman purchases milk at $5 per litre and mixes 4 litres of water in it. By selling the resultant mixture at the rate of $6 per litre, he earns a profit of 40%. The amount of mixture he had with him to sell was:

How much water must be added to 60 litres of milk at 1.5 litres for $20 So as to have a mixture worth a litre?

A 60 litre mixture of sugar and water contains sugar and water in the ratio 2:3. How many litres of the mixture should be replaced by sugar so that the ratio of sugar and water becomes 1:1?

A vessel contains a mixture of milk and water in the ratio of 14 : 3. Now, 25.5 litres of the mixture is taken out from the vessel and 2.5 litres of pure water and5 litres of pure milk is added to the mixture. If the resultant mixture contains 20% water, what was the initial quantity of mixture in the vessel before there placement ? (in litres)

A tank contains 30 litres of diesel, 6 litres are drawn out and filled by kerosene. This process is repeated three times. What will be the proportion of diesel to kerosene in the resulting mixture ?

Recently,  Johnson City replaced all paper-towel dispensers in lavatories of city buildings with electric hand dryers . The city estimates that in about fifteen years the amount that would otherwise have been spent on the purchase and disposal of paper towels will begin to exceed the cost of purchasing, installing, and operating the electric dryers. Therefore,   despite high initial costs, replacing paper towels with electric hand dryers will be to the city’s long-term economic advantage.

Which of the following is an assumption on which the argument depends?

The function f is defined by for all positive numbers x. If for some positive numbers t and u, what is t in terms of u?