Solution:
Let us say, the average speed of passenger train = x km/h.
Average speed of express train = (x + 11) km/h
Given, time taken by the express train to cover 132 km is 1 hour less than the passenger train to cover the same distance. Therefore,
$132\left( x+11-x \right)/\left( x\left( x+11 \right) \right)\text{ }=\text{ }1$
$132\text{ }\times \text{ }11\text{ }/\left( x\left( x+11 \right) \right)\text{ }=\text{ }1$
$\Rightarrow 132\text{ }\times \text{ }11\text{ }=~x\left( x~+\text{ }11 \right)$
$\Rightarrow ~{{x}^{2}}~+\text{ }11x~\text{ }1452\text{ }=\text{ }0$
$\Rightarrow ~{{x}^{2}}~+~\text{ }44x~-33x~-1452\text{ }=\text{ }0$
$\Rightarrow ~x\left( x~+\text{ }44 \right)\text{ }-33\left( x~+\text{ }44 \right)\text{ }=\text{ }0$
$\Rightarrow \left( x~+\text{ }44 \right)\left( x~\text{ }33 \right)\text{ }=\text{ }0$
$\Rightarrow ~x~=\text{ }\text{ }44,\text{ }33$
As we know, Speed cannot be negative.
Therefore, the speed of the passenger train will be 33 km/h and thus, the speed of the express train will be 33 + 11 = 44 km/h.