A body covers half the distance with a speed of $20\text{m/s}$ and the other half with $30\text{m/s}$. The average speed of the body during the whole journey is

Let the total distance be $2d$, so each half of the journey represents a distance of $d$.
$$\text{Time taken for the first half, }{t}_1=\frac{d}{v_1}=\frac{d}{20}$$

$$\text{Time taken for the second half, }{t}_2=\frac{d}{v_2}=\frac{d}{30}$$

The general formula for average speed ($v_{\text{avg}}$) over equal distance segments reduces to the harmonic mean of the speeds:

$$v_{\text{avg}}=\frac{\text{Total Distance}}{\text{Total Time}}=\frac{2d}{t_1+t_2}=\frac{2v_1{v}_2}{v_1+v_2}$$

Substitute $v_1=20\text{m/s}$ and $v_2=30\text{m/s}$ into the formula:

$$v_{\text{avg}}=\frac{2\times 20\times 30}{20+30}$$

$$v_{\text{avg}}=\frac{1200}{50}=24\text{m/s}$$