A car is moving towards a high cliff. The car driver sounds a horn of frequency 'f'. The reflected sound heard by the driver has a frequency 2f. If 'v' be the velocity of sound then the velocity of the car, in the same velocity units, will be -

The problem is done in two stages. First the cliff acts as a stationary observer receiving sound from the moving source (the car).
Frequency received by the cliff: $f' = \left(\dfrac{v}{v - v_{car}}\right) f$
Next, the cliff acts as a stationary source of frequency $f'$, and the driver is an observer moving towards it.
Frequency heard by the driver: $f'' = \left(\dfrac{v + v_{car}}{v}\right) f' = \left(\dfrac{v + v_{car}}{v - v_{car}}\right) f$
Given $f'' = 2f$: $\dfrac{v + v_{car}}{v - v_{car}} = 2$
$\Rightarrow v + v_{car} = 2v - 2v_{car}$
$\Rightarrow 3v_{car} = v$
$\Rightarrow v_{car} = \dfrac{v}{3}$