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. \[ \text{Ratio}=75:75=1:1. \] \[ \boxed{1:1} \] 

Answer 2

Instead of setting up the equation in terms of the distance covered by car, we can set it up in terms of the time spent on each vehicle, and check each option against the result.

1. Option A (\(2:3\)): Let \(t_1\) be the time (in hours) spent travelling by car and \(t_2\) the time by rickshaw, with \(t_1+t_2=10\). The total distance is \[ 20t_1+12t_2=150. \] Substituting \(t_1=10-t_2\): \[ 20(10-t_2)+12t_2=150\;\Rightarrow\;200-8t_2=150\;\Rightarrow\;t_2=6.25,\ t_1=3.75. \] Distance by car \(=20(3.75)=75\) km, by rickshaw \(=12(6.25)=75\) km, giving a ratio of \(75:75=1:1\), not \(2:3\), so this option is incorrect.
2. Option B (\(4:5\)): This does not match the computed \(75:75\) ratio, so it is incorrect.
3. Option C (\(1:1\)): As computed, both distances come out to exactly \(75\) km each, giving a ratio of \(1:1\), which matches this option exactly.
4. Option D (none of these): Since option C exactly matches the ratio obtained from the calculation, this option cannot be correct.

Solving with time as the variable confirms that the car and rickshaw each covered \(75\) km, a ratio of \(1:1\).

Hence, the correct answer is option C: \(1:1\).