In what ratio must a grocer mix two varieties of tea worth $Rs. 60$ per $kg$ and $Rs. 65$ per $kg$ so that by selling the mixture at $Rs. 68.20$ per $kg$ he may gain $10\%$?

The acid and water in two vessels $A$ and $B$ are in the ratio $4:3$ and $2:3$. In what ratio should the liquids in both the vessels be mixed to obtain a new mixture in vessel $C$ containing half acid and half water?

In an examination out of $900$ students,$85 \%$ of the boys and $70 \%$ of the girls passed. How many girls appeared in the examination,if the total pass percentage was $75 \% ?$

$A$ pot contains $81$ $\text{litres}$ of pure milk. $\frac{1}{3}$ of the milk is replaced by the same amount of water. Again $\frac{1}{3}$ of the mixture is replaced by that amount of water. The ratio of the milk and water in the new mixture is?

Three bottles of equal capacity contain mixtures of milk and water in the ratios $2:5$,$3:4$,and $4:5$ respectively. These three bottles are emptied into a large bottle. What will be the ratio of milk and water respectively in the large bottle?

Aditya and Sanjay started a business investing $45000$ and $30000$ respectively. What will be the ratio between their profit?