The ratio of the distance between two place A and B to the distance between places B and C is 3 : 5. A man travels from A to B at a speed of x km/h and from B to C at a speed of 50 km/h. If his average speed for the entire journey is 40 km/h, then what is the value of (x - 10) : (x + 1)?

Answer: Option B

Let the distance between A and B to the distance between B and C be 3a and 5a respectively
According to the question
Time taken by man to travel from A and B at a speed of x km/hr = $$\frac{3a}{x}$$
Time taken by man to travel from B and C at a speed of 50 km/hr = $$\frac{5a}{50}\Rightarrow \frac{a}{10}$$
Average speed of the entire journey = $$\frac{\text{Total distance}}{\text{Total time taken}}$$
$$\begin{array}{rl}& \Rightarrow \frac{3a+5a}{\frac{3a}{x}+\frac{a}{10}}=40\\ & \Rightarrow \frac{8a}{\frac{3a}{x}+\frac{a}{10}}=40\\ & \Rightarrow 8a=40a\left(\frac{3}{x}+\frac{1}{10}\right)\\ & \Rightarrow \frac{1}{5}=\frac{30+x}{10x}\\ & \Rightarrow 2x=30+x\\ & \Rightarrow 2x-x=30\\ & \Rightarrow x=30\text{km/hr}\end{array}$$
Now,
The value of (x - 10) : (x + 1) = (30 - 10) : (30 + 1)
⇒ 20 : 31
∴ The required value is 20 : 31