In a room, there are $n$ persons whose average height is $160 \ \text{cm}$. If $m$ more persons, whose average height is $172 \ \text{cm}$, enter the room, then the average height of all persons in the room becomes $164 \ \text{cm}$. Then $m: n$ is

In a bowl containing 60 ml orange juice, 40 ml of water is poured. Thereafter, 100 ml of apple juice is poured to make a fruit punch. Madhu drinks 50 ml of this fruit punch and comments that the proportion of orange juice needs to be higher for better taste. How much orange juice should be poured into the fruit punch that remained, in order to bring up the level of orange juice to 50 percentage?

Fifty litres of a mixture of milk and water contains 30 percent of water. This mixture is added to eighty litres of another mixture of milk and water that contains 20 percent of water. Then, how many litres of water should be added to the resulting mixture to obtain a final mixture that contains 25 percent of water?

An alloy $P$ has copper and zinc in the proportion of $5:2$ (by weight), while another alloy $Q$ has the same metals in the proportion of $3:4$ (by weight). If these two alloys are mixed in the proportion of $a:b$ (by weight), a new alloy $R$ is formed, which has equal contents of copper and zinc. Then, the proportion of copper and zinc in the alloy $S$, formed by mixing the two alloys $P$ and $Q$ in the proportion of $b:a$ (by weight) is