In what ratio must a grocer mix two varieties of pulses costing $Rs. 15$ and $Rs. 20$ per $kg$ respectively so as to get a mixture worth $Rs. 16.5$ per $kg$?

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 $kg$?

There are $65$ students in a class. $39$ rupees are distributed among them so that each boy gets $80$ Paise and each girl gets $30$ Paise. Find the number of boys and girls in that class.

How much water should be added to $14$ litres of milk worth ₹ $5.40$ a litre so that the value of the mixture may be ₹ $4.20$ a litre? (in litres)

$A$ 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 $\text{km}$)

$A$ trader has $50 \text{ kg}$ of rice,a part of which he sells at $10 \%$ profit and the rest at $5 \%$ loss. He gains $7 \%$ on the whole. What is the quantity sold at $10 \%$ gain and $5 \%$ loss? (in $\text{kg}$)