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)?

Solution (By Examveda Team)

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 = $$\frac{{{\text{Total distance}}}}{{{\text{Total time taken}}}}$$
$$\eqalign{ & \Rightarrow \frac{{3a + 5a}}{{\frac{{3a}}{x} + \frac{a}{{10}}}} = 40 \cr & \Rightarrow \frac{{8a}}{{\frac{{3a}}{x} + \frac{a}{{10}}}} = 40 \cr & \Rightarrow 8a = 40a\left( {\frac{3}{x} + \frac{1}{{10}}} \right) \cr & \Rightarrow \frac{1}{5} = \frac{{30 + x}}{{10x}} \cr & \Rightarrow 2x = 30 + x \cr & \Rightarrow 2x - x = 30 \cr & \Rightarrow x = 30\,{\text{km/hr}} \cr} $$
Now,
The value of (x - 10) : (x + 1) = (30 - 10) : (30 + 1)
⇒ 20 : 31
∴ The required value is 20 : 31