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 $25: 62?$

Nine litres of water are drawn from a container full of water and it is then filled with milk. Nine litres of mixture are drawn and the container is again filled with milk. The ratio of the quantity of water now left in the container to that of the milk in it is $16:9$. How much liquid does the container hold? (in $litres$)

Find the ratio in which rice at $Rs. 7.20$ per $kg$ should be mixed with rice at $Rs. 5.70$ per $kg$ to produce a mixture worth $Rs. 6.30$ per $kg$.

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?

$A$ dishonest trader professes to sell his article at cost price but he uses $900 \, g$ weight instead of $1 \, kg$. What is the percentage gain of the trader in this trade?

$A$ sum of $Rs. 41$ was divided among $50$ children. Each boy gets $90$ paise and each girl $65$ paise. The number of boys is?