An alloy of gold and silver is taken in the ratio of $1:2$, and another alloy of the same metals is taken in the ratio of $2:3$. How many parts of the two alloys must be taken to obtain a new alloy consisting of gold and silver that are in the ratio $3:5$?
 

Two boxes A and B were filled with a mixture of rice and dal—in A in the ratio of $5:3$, and in B in the ratio of $7:3$. What quantity must be taken from the first to form a mixture that shall contain $6 \mathrm{kg}$ of rice and $3 \mathrm{kg}$ of dal?

A person buys $18$ local tickets for $110$. Each first class ticket costs $10$ and each second class ticket costs $3$. What will another lot of $18$ tickets in which the number of first class and second class tickets are interchanged cost?
 

Two jars having a capacity of $3$ and $5 \mathrm{litres}$ respectively are filled with mixtures of milk and water. In the smaller jar $25\%$ of the mixture is milk and in the larger $25\%$ of the mixture is water. The jars are emptied into a $10 \mathrm{litre}$ cask whose remaining capacity is filled up with water. Find the percentage of milk in the cask.
 

Two cubes of bronze have their total weight equivalent to $60 \mathrm{kg}$. The first piece contains $10 \mathrm{kg}$ of pure zinc and the second piece contains $8 \mathrm{kg}$ of pure zinc.What is the percentage of zinc in the first piece of bronze if the second piece contains $15$ percent more zinc than the first?
 

From a vessel filled up with pure spirit to the brim, two litres of spirit was removed and $2$litres of water were added. After the solution was mixed, $2$ litres of the mixture was poured off and again $2$litres of water was added. The solution was stirred again and $2$ litres of the mixture was removed and $2$ litres of water was added. As a result of the above operations, the volume of water in the vessel increased by $3$ litres than the volume of spirit remaining in it. How many litres of spirit and water were there in the vessel after the above procedure was carried out?

There are two qualities of milk-Amul and Sudha having different prices per litre, their volumes being$130$ litres and$180$ litres respectively. After equal amounts of milk was removed from both, the milk removed from Amul was added to Sudha and vice-versa. The resulting two types of milk now have the same price. Find the amount of milk drawn out from each type of milk?

Assume that the rate of consumption of coal by a locomotive varies as the square of the speed and is $1000$ kg per hour when the speed is $60$ km per hour. If the coal costs the railway company $₹15/100$ Kg and if the other expenses of the train be $12$ per hour, find a formula for the cost in paise per kilometre when the speed is $\mathrm{S}$ km per hour.