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 $3:2$?

An amount of ₹ $70,000$ was lent at $6 \%$ per annum and the remaining at $4 \%$ per annum. If the total simple interest from both the fractions in $5 \text{ years}$ was ₹ $16,000$,the sum lent at $6 \%$ per annum was (in ₹). (in $,000$)

$A$ shopkeeper bought $15 \text{ kg}$ of rice at the rate of $Rs. 29$ per $\text{kg}$ and $25 \text{ kg}$ of rice at the rate of $Rs. 20$ per $\text{kg}$. He sold the mixture of both types of rice at the rate of $Rs. 27$ per $\text{kg}$. His profit in this transaction is (in $Rs.$)

$A$ sugar solution of $3$ $litre$ contains $60 \%$ sugar. One litre of water is added to this solution. Then the percentage of sugar in the new solution is (in $\%$)

In a mixture of $75 \, litres$,the ratio of milk to water is $2:1$. The amount of water to be further added to the mixture so as to make the ratio of milk to water $1:2$ will be (in $litres$):

In a $40 \, L$ mixture of milk and water,the ratio of milk to water is $7:1$. In order to make the ratio of milk and water $3:1$,the quantity of water (in $litres$) that should be added to the mixture will be: