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

Let distance by car $=x$, by rickshaw $=150-x$.
Time by car $=\dfrac{x}{20}$, by rickshaw $=\dfrac{150-x}{12}$.
Total time $=10$ hours: \[ \frac{x}{20}+\frac{150-x}{12}=10. \] Multiply through by $60$: \[ 3x+5(150-x)=600. \] \[ 3x+750-5x=600 \quad\Rightarrow\quad -2x=-150 \quad\Rightarrow\quad x=75. \] So both car and rickshaw covered $75$ km each. \[ \text{Ratio}=75:75=1:1. \] \[ \boxed{1:1} \]