A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.

224 km

Let the total distance = $D\text{ km}$.

Then each half of the journey is $\frac{D}{2}\text{ km}$.

Time taken for the first half:

$\frac{D/2}{21} = \frac{D}{42}$

Time taken for the second half:

$\frac{D/2}{24} = \frac{D}{48}$

Total time is $10\text{ hours}$:

$\frac{D}{42} + \frac{D}{48} = 10$

Taking LCM 336:

$\frac{8D + 7D}{336} = 10$

$\frac{15D}{336} = 10$

$D = \frac{10 \times 336}{15} = 224\text{ km}$