Piyush covers a certain distance on bike. Had he moved 3 km/h faster, he would have taken 20 min less. If he had moved 2 km/h slower, he would have taken 20 min more. The distance covered (in km) is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 20 KM
For a fixed distance, time = distance ÷ speed, so each change of speed gives an equation for the difference in time. Let the distance be \(d\) km and the usual speed \(v\) km/h; 20 min \(=\frac{1}{3}\) h.
Equation (1) (3 km/h faster saves 20 min):
\(\displaystyle\frac{d}{v}-\frac{d}{v+3}=\frac{1}{3}\)
\(\displaystyle\frac{3d}{v(v+3)}=\frac{1}{3}\)
So \(9d=v(v+3)\) (1)
Equation (2) (2 km/h slower costs 20 min):
\(\displaystyle\frac{d}{v-2}-\frac{d}{v}=\frac{1}{3}\)
\(\displaystyle\frac{2d}{v(v-2)}=\frac{1}{3}\)
So \(6d=v(v-2)\) (2)
The speed (dividing (1) by (2), \(d\) and \(v\) cancel):
\(\displaystyle\frac{9}{6}=\frac{v+3}{v-2}\)
So \(3(v-2)=2(v+3)\)
\(v=12\) km/h
The distance (putting \(v=12\) in (1)):
\(9d=12\times15=180\)
\(d=20\) km