H S Hall and S R Knight Solutions for Chapter: Proportion, Exercise 1: Examples. II .

Find the mean proportional between $360a^4$ and $250a^2{b}^2.$

Two casks $A$ and $B$ when filled with two kinds of sherry, mixed in the cask $A$ in the ratio of $2:7$, and in the cask $B$ in the ratio of $1:5$, what quantity must be taken from each to form a mixture which shall consist of $10$ litres of one kind and $45$ litres of the other?

Nine litres are drawn from a cask full of wine, it is then filled with water then nine litres of the mixture are drawn, and the cask is again filled with water. If the quantity of wine now in the cask be to the quantity of water in it as $16$ to $9$, how much does the cask hold?

If four positive quantities are in continued proportion, show that the difference between the first and the last is at least three times as great as the difference between the other two.

In England the population increased by $15.9$ percent between $1871$ and $1881,$ if the town population increased $18$ percent and the country population $4$ percent. Compare the town and country populations in $1871.$

In a certain country the consumption of tea is five times the consumption of coffee. If $a$ percent more tea and $b$ percent more coffee were consumed, the aggregate consumed would be $7c$ percent more, but if $b$ percent more tea and $a$ percent more coffee were consumed, the aggregate amount consumed would be $3c$ percent more. Compare $a$ and $b.$

Brass is an alloy of copper and zinc; bronze is an alloy containing $80$ percent of copper, $4$ percent of zinc and $16$ percent of tin. A fused mass of brass and bronze is found to contain $74$ percent of copper, $16$ percent of zinc and $10$ percent of tin, find the ratio of copper to zinc in the composition of brass.

A crew can row a certain course up stream in $84$ minutes, they can row the same course down the stream in $9$ minutes less than they could row it in still water, how long would they take to row down water stream?