Answer
$T=82.2 C^{\circ}$
Work Step by Step
We know that the heat gained by the glass cup is given as
$q_{glass}=m_{glass}.C_{glass}.\Delta T_{glass}$
$\implies q_{glass}=(250)(0.840)(T-20)$
$\implies q_{glass}=(210)(T-20)$
Similarly, the heat released by the hot water is given as
$q_{H_2O}=m_{H_2O}.C_{H_2O}.\Delta T_{H_2O}$
$\implies q_{H_2O}=(400)(4.184)(90-T)$
$q_{H_2O}=(1673.6)(90-T)$
We know that the heat released by the hot water is equal to the heat gained by the glass that is
$(210)(T-20)=(1673.6)(90-T)$
This simplifies to:
$T=82.2 C^{\circ}$
