The ratio of the distance between places A and B to the distance between places B and C is 3 : 5. A man travels from A to B at \(x\) km/hr and from B to C at 50 km/hr. If his average speed for the entire journey is 40 km/hr, what is \((x-20):(x+2)\)?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 5 : 16
Take the distances as \(3d\) and \(5d\). The average speed is total distance divided by total time, which gives an equation for \(x\).
Total distance \(=8d\); total time \(\displaystyle =\frac{3d}{x}+\frac{5d}{50}=\frac{3d}{x}+\frac{d}{10}\)
\(\displaystyle \frac{8d}{\frac{3d}{x}+\frac{d}{10}}=40\), so \(\displaystyle \frac{3}{x}+\frac{1}{10}=\frac{8}{40}=\frac{1}{5}\)
\(\displaystyle \frac{3}{x}=\frac{1}{10}\), so \(x=30\)
\((x-20):(x+2)=10:32=5:16\)