An alloy of zinc, tin and copper contains $90\%$ of copper, $7\%$ of zinc and $3\%$of tin. A second alloy of copper and tin only is melted with the first, and the mixture contains $85\%$ copper, $5\%$ zinc and $10\%$ of tin. Find the percentage of tin in the second alloy.

Two metals $X$ and $Y$ are to be used for making two different alloys. If the ratio by weight of $X:Y$ in the first alloy is $6:5$ and that in the second is $7:13$, how many kg of metal $X$ must be melted along with $11 \mathrm{kg}$ of the first alloy and $20 \mathrm{kg}$ of the second to produce a new alloy containing $40\%$ of metal $Y$?

Two vessels contain mixtures of juice and water in the ratio of $8$ to $3$ and $5$ to $1$, respectively. In what ratio must liquid be drawn from each vessel to give a mixture in the ratio of $4$ to $1$?

How many $\mathrm{kg}$ of tea at $Rs.62.5$ per $\mathrm{kg}$ must be added to $100 \mathrm{kg}$ of tea at $Rs.78$ per $\mathrm{kg}$ so that a profit of$33.33\%$ is made by selling the mixture at $Rs.94$ per $\mathrm{kg}$?

A pot contains a mixture of milk and water in the ratio of $4:3$, and another pot contains a mixture of milk and water in the ratio of $3:4$. How many seers of the second mixture should be added to $7$ seers of the first so that the milk and water in the resulting mixture be $6:5$?

A merchant has $100 \mathrm{kg}$ of sugar, part of which he sells at $7\%$ profit and the rest at $17\%$ profit. He gains $10\%$ on the whole. How much is sold at $17\%$?

A man travelled a distance of $80 \mathrm{km}$ in $7$ hours partly on foot at the rate of $8 \mathrm{km}$ per hour and partly on bicycle at $16 \mathrm{km}$ per hour. Find the distance travelled on foot.

A merchant borrowed $Rs.2500$ from two money lenders. For one loan he paid $8\%$ per annum and for the other $6\%$ per annum. The total interest paid for $1$year was $Rs.180$. How much did he borrow at each rate?

A tea merchant buys two kinds of tea, the price of the first kind being twice that of the second. He sells the mixture at $Rs.17.50$ per $\mathrm{kg}$, thereby making a profit of $25\%$. If the ratio of first and second kinds of tea in the mixture be $2:3$, find the cost price of each kind of tea?