How much tea at $Rs. 4$ a $kg$ should be added to $15 \, kg$ of tea at $Rs. 10$ per $kg$ so that the mixture is worth $Rs. 6.50$ a $kg$? (in $kg$)

$A$ man has $60$ pens. He sells some of these at a profit of $12 \%$ and the rest at $8 \%$ loss. On the whole,he gets a profit of $11 \%$. How many pens were sold at $12 \%$ profit?

$A$ person travels $285 \text{ km}$ in $6 \text{ hours}$ in two stages. In the first part of the journey,he travels by bus at a speed of $40 \text{ km/h}$. In the second part of the journey,he travels by train at a speed of $55 \text{ km/h}$. How much distance did he travel by train? (in $\text{km}$)

$A$ man has $40 \ kg$ of tea,a part of which he sells at $5 \%$ loss and the rest at the cost price. In this business,he incurs a total loss of $3 \%$. Find the quantity of tea which he sells at the cost price (in $kg$).

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 $20\%$?

In a mixture of milk and water of volume $30$ $L$,the ratio of milk and water is $8:7$. How much water should be added to the mixture to make the ratio $4:5$? (in $L$)