$400 \, gm$ of salt solution has $40 \%$ salt in it. How much salt should be added to make the concentration $50 \%$ in the solution?

Two casks of $48$ $litres$ and $42$ $litres$ are filled with mixtures of wine and water,the proportions in the two casks being respectively $13:7$ and $18:17$. If the contents of the two casks are mixed,and $20$ $litres$ of water is added to the whole,what will be the proportion of wine to water in the resultant mixture?

$A$ bottle contains $81$ 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 the same amount of water. The ratio of the milk and water in the new mixture is

There are $65$ students in a class. $39$ rupees are distributed among them so that each boy gets $80$ Paise and each girl gets $30$ Paise. Find the number of boys and girls in that class.

Rama mixes $20 \%$ of kerosene to his petrol and then he sells the whole mixture at the price of petrol. If the cost price of the kerosene is $40 \%$ of the $CP$ of petrol,what is the net profit percentage (in $\%$)?

$A$ person has ₹ $5000$. He invests a part of it at $3 \%$ per annum and the remainder at $8 \%$ per annum simple interest. His total income in $3$ years is ₹ $750$. Find the sum invested at different rates of interest (in ₹).