[prasannab13]

Why boiling point is directly proportional to external pressure  and inversely proportional to vapour pressure?

As vapour pressure increases ,external pressure also should be same as vapour pressure to determine boiling point of liquid.

[Hunt]

When the external pressure increases, the vapour pressure increases exponentially . Since the vapour pressure and the boiling temperature are related by the clausius-clapeyron equation :

dP / dT = Delta_vapH P / RT² , slope > 0

Then the equilibrium boiling temp rises too.

There are no directly/inversely proportional realtions between the boiling tempreature and the external pressure / vapour pressure. Even in the simplest cases , you'll get logarithmic / exponential  relations.