A car travelling at 108 km h^ -1 encounters another car ahead of it...

Speed of the first car (source), $v_s = 108 \text{ km h}^{-1} = 108 \times \dfrac{5}{18} \text{ m s}^{-1} = 30 \text{ m s}^{-1}$

Speed of the second car (observer), $v_o = 72 \text{ km h}^{-1} = 72 \times \dfrac{5}{18} \text{ m s}^{-1} = 20 \text{ m s}^{-1}$

Actual frequency of the horn, $f = 800 \text{ Hz}$

Speed of sound, $v = 330 \text{ m s}^{-1}$

The source is moving towards the observer and the observer is moving away from the source.

Using the Doppler effect formula for apparent frequency:

f' = f \left(\dfrac{v - v_o}{v - v_s} \right)

Substituting the given values:

$f' = 800 \left( \dfrac{330 - 20}{330 - 30} \right)$

f' = 800 \left(\dfrac{310}{300} \right)

$f' = 800 \times$\dfrac{31}{30}

$f' =$\dfrac{2480}{3} \approx$826.67 \text{ Hz}$

Rounding off to the nearest integer, the apparent frequency is $827 \text{ Hz}$.