Multiple choice

Ankita travels $14 km$ to her home partly by rickshaw and partly by bus. She takes half an hour if she travels $2 km$ by rickshaw, and the remaining distance by bus. On the other hand, if she travels $4 km$ by rickshaw and the remaining distance by bus, she takes $9$ minutes longer. Find the speed of the rickshaw in km/hr.

  1. $10$
  2. $14$
  3. $13$
  4. $7$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let r be rickshaw speed and b be bus speed. 2/r + 12/b = 0.5. 4/r + 10/b = 0.5 + 9/60 = 0.65. Solving the system: 4/r + 24/b = 1. Subtracting: 14/b = 0.35, so b = 40. 2/r + 12/40 = 0.5 => 2/r = 0.5 - 0.3 = 0.2 => r = 10.

AI explanation

Let the speed of the rickshaw be x km/hr and the speed of the bus be y km/hr. In the first scenario, the time taken is 2/x + 12/y = 0.5 hours. In the second scenario, the time taken is 4/x + 10/y = 0.65 hours, since 9 minutes is 0.15 hours. Multiplying the first equation by 2 gives 4/x + 24/y = 1, and subtracting the second equation from this yields 14/y = 0.35, meaning the speed of the bus is 40 km/hr. Substituting y back into the first equation gives 2/x + 12/40 = 0.5, so 2/x = 0.2, which means the speed of the rickshaw is 10 km/hr.

Keep practicing — related questions