Two types of alloys contain gold and silver in the ratio of $7: 22$ and $21: 37.$ In what ratio should these alloys be mixed,so as to have a new alloy in which gold and silver would exist in the ratio $25: 62?$

$A$ sugar solution of $3$ $litre$ contains $60 \%$ sugar. One litre of water is added to this solution. Then the percentage of sugar in the new solution is (in $\%$)

$8$ litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in the cask to that of the water is $16$:$65$. How much wine did the cask hold originally? (in litres)

$A$ sum of ₹ $64$ is made up of $80$ coins which are either $100$ $paise$ or $50$ $paise$ coins. How many coins are of $50$ $paise$?

Sourav purchased $30 \text{ kg}$ of rice at the rate of $₹ 10$ per $\text{kg}$ and $35 \text{ kg}$ at the rate of $₹ 11$ per $\text{kg}$. He mixed the two. At what price per $\text{kg}$ should he sell the mixture to make a $30\%$ profit in the transaction?

The ratio of alcohol and water in $40$ $litres$ of mixture is $5:3$. Then $8$ $litres$ of the mixture is removed and replaced with water. Now,the ratio of the alcohol and water in the resultant mixture is