Question

Avinash covered 150 km in 10 hours. The first part of his journey he covered by car, then by rickshaw. Speed of car and rickshaw are $20$ km/hr and $12$ km/hr respectively. Find the ratio of distances covered by car and rickshaw.

• A. $2:3$
• B. $4:5$
• C. $1:1$
• D. None of these

Hint:

For distance-time-speed problems, always use $t=\tfrac{d}{v}$, then add times to match total. Ratios often simplify elegantly.

Answer 1

The Correct Option is C

Step 1: Let time by car \(=t_1\), by rickshaw \(=t_2\), with \(t_1+t_2=10\).

Step 2: Distance equation: \[ 20t_1+12t_2=150 \] Substituting \(t_1=10-t_2\) gives \(t_2=6.25\), \(t_1=3.75\).

Step 3: Distances: car \(=20(3.75)=75\) km, rickshaw \(=12(6.25)=75\) km. \[ \text{Ratio}=\boxed{1:1} \]