Calculate the fourth proportional to the numbers $286, 78, 1342$.

The ratio of the number of boys and girls in a school of $720$ students is $7: 5$. How many more girls should be admitted to make the ratio $1: 1$?

In a college,$150$ students of $MBA$ are enrolled. The ratio of boys to girls is $7:8$. There are three disciplines in the college: Marketing,$HR$,and Finance. In the Marketing discipline,there are $50\%$ of the total girls and $40\%$ of the total boys. In the $HR$ discipline,there are $30\%$ of the total girls and $30\%$ of the total boys. In the Finance discipline,there are $20\%$ of the total girls and $30\%$ of the total boys. $7$ boys and $9$ girls are in both $HR$ and Marketing. $6$ boys and $7$ girls are in both $HR$ and Finance. $5$ boys and $8$ girls are in both Marketing and Finance. $2$ boys and $3$ girls are enrolled in all three disciplines. What is the ratio of boys to girls only in the Marketing discipline?

There is $1000 \, \text{litres}$ of milk in a pot. $100 \, \text{litres}$ of milk is taken out and the same amount of water is poured into it. Again, $200 \, \text{litres}$ of the mixture is taken out and the same amount of water is poured into it, and finally, $400 \, \text{litres}$ of the mixture is taken out and the same amount of water is poured into it. What is the amount of milk in the resulting mixture?

$A$ box contains ₹ $56$ in the form of coins of one-rupee,$50-paise$ and $25-paise$. The number of $50-paise$ coins is double the number of $25-paise$ coins and four times the number of one-rupee coins. How many $50-paise$ coins are there in the box?

$A$ mixture of milk and water is kept in two separate containers. The ratio of milk to water in one container is $5:1$ and in the other container is $7:2$. In what ratio should the mixtures from these two containers be mixed so that the quantity of milk in the new mixture becomes $80\%$?