Some amount out of ₹$7000$ was lent at $6 \%$ $p.a.$ and the remaining at $4 \%$ $p.a.$ If the total simple interest from both the fractions in $5$ $years$ was ₹$1600$,the sum lent at $6 \%$ $p.a.$ was (in ₹).

$A$ 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?

In what ratio must a person mix three kinds of tea costing $Rs. 60$ per $kg$,$Rs. 75$ per $kg$,and $Rs. 100$ per $kg$ so that the resultant mixture when sold at $Rs. 96$ per $kg$ yields a profit of $20\%$?

Vessels $A$ and $B$ contain acid and water in the ratios $4:3$ and $5:3$ respectively. In what ratio must these mixtures be mixed to obtain a new mixture in vessel $C$ containing acid and water in the ratio $3:2$?

In what ratio must water be mixed with milk to gain $16 \%$ on selling the mixture at cost price?

Solution $A$ contains $10 \%$ acid and solution $B$ contains $30 \%$ acid. In what ratio should solution $A$ be mixed with solution $B$ to obtain a mixture with $25 \%$ acid?