Two candles of the same height are lit at the same time. The first is consumed in $6 \mathrm{h}$ and the second in $4 \mathrm{h}.$ Assuming that each candle burns at a constant rate, in how many hours after being lit does the ratio between the first and the second candle become $2:1?$

$\mathrm{Rs}.1,800$ is to be divided among three friends Varun, Shyam and Pawan in the ratio $2:3:5.$ Find the share of Shyam.

On a scale of a map, $6 \mathrm{mm}$ represents $12 \mathrm{km}.$ If the distance between Lucknow and Kanpur on the map is $40 \mathrm{mm},$ the actual distance between these cities is _____.

The salaries of Raju and Sumit are in the ratio $2:3.$ If their salaries are increased by $\mathrm{Rs}.4,000$ each, the new ratio becomes $4:5.$ What was Sumit's salary before the increase?

The ratio of two numbers is $10$ and their difference is $18.$ What is the value of the smaller number?