Question on working of turbocharger and intercooler From what I read in my notes. In a turbocharger,the gas from the exhaust is used to drive a turbine which in turn drives a compressor. This compressor compresses free air from the surrounding. The compression of air cause a increase in temperature and lowers density of air. Thus we use a intercooler.
But wouldn't using the intercooler reduce the pressure with the decrease in temperature and also reduce the efficiency of the engine? Considering the fact that a engine needs to reach a critical temperature for best possible fuel efficiency.
 A: 
But wouldn't using the intercooler reduce the pressure with the
decrease in temperature and also reduce the efficiency of the engine?

Reduction of pressure can reduce efficiency of the engine , all else being equal.
But here, all else is not equal. The intercooler reduces pressure , but at the same time reduces temperature of the intake charge as well, which increases density of air, hence allowing more air into the engine, which increases power.
So, the effect of  intercooler's decrease of pressure is more than made up for by the decrease in temperature and hence results in a net increase in density.
From wikipedia,

Passing a compressed and heated intake charge through an intercooler
reduces its temperature (due to heat rejection) and pressure (due to
flow restriction of fins). If the device is properly engineered, the
relative decrease in temperature is greater than the relative loss in
pressure, resulting in a net increase in density.

Also, you said

Considering the fact that a engine needs to reach a critical
temperature for best possible fuel efficiency.

Intercooler cools down the intake charge, it does not cool the engine . A cooler intake charge allows greater density of air . More air means better burning of the fuel and hence, better efficiency .
