How many kilograms of sugar costing $Rs. 9$ per $kg$ must be mixed with $27\, kg$ of sugar costing $Rs. 7$ per $kg$ so that there may be a gain of $10\%$ by selling the mixture at $Rs. 9.24$ per $kg$?

In what proportion must a grocer mix sugar at ₹ $12$ per $kg$ and ₹ $7$ per $kg$ so as to make a mixture worth ₹ $8$ per $kg$?

In a mixture of $60\, L$,the ratio of acid and water is $2:1$. If the ratio of acid and water is to be $1:2$,then the amount of water (in $litres$) to be added to the mixture is:

The average weekly salary per head of all employees (supervisors and labourers) is ₹ $100$. The average weekly salary per head of all the supervisors is ₹ $600$,while the average weekly salary per head of all the labourers is ₹ $75$. Find out the number of supervisors in the factory if there are $840$ labourers in it.

Haresh earned ₹ $4000$ per month. From the last month,his income increased by $8\%$. Due to a rise in prices,his expenditure also increased by $12\%$ and his savings decreased by $4\%$. Find his increased expenditure and initial savings.

$A$ tub contains a mixture of two liquids $P$ and $Q$ in the ratio of $4:1$. When $10 \, L$ of the mixture is taken out and $10 \, L$ of liquid $Q$ is poured into the tub,the ratio becomes $2:3$. How many litres of liquid $P$ were contained in the tub initially?