$A$ 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 ₹).

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

$80 \text{ litre}$ mixture of milk and water contains $10 \%$ milk. How much milk (in $\text{litre}$) must be added to make water percentage in the mixture $80 \% ?$

$A$ $12 \text{ litres}$ cylinder contains a mixture of oxygen and nitrogen,the volume of oxygen being $40 \%$ of the total volume. $A$ few litres of the mixture is released and an equal amount of nitrogen is added. Then,the same amount of the mixture as before is released and replaced by nitrogen for the $second$ time. As a result,the oxygen content becomes $10 \%$ of the total volume. How many $litres$ of the mixture is released each time?

Milk and water are mixed in vessel $A$ in the ratio of $5:2$ and in vessel $B$ in the ratio of $8:5$. In what ratio should quantities be taken from the two vessels so as to form a mixture in which milk and water will be in the ratio of $9:4$?

$A$ merchant mixes three varieties of rice costing $Rs. 20$ per $kg$,$Rs. 24$ per $kg$,and $Rs. 30$ per $kg$ and sells the mixture at a profit of $20\%$ at $Rs. 30$ per $kg$. How many $kgs$ of the second variety will be in the mixture if $2$ $kgs$ of the third variety is there in the mixture?