Question

During the shooting of a super hit film, ‘MARD’ Amitabh Bachchan was waiting for his beloved Amrita Singh with his dog. When he saw her approaching, the dog was excited and dashed to her then back to master and so on, never stopping. How far would you estimate the dog ran if his speed is 30 km/h, and each of them walked at 4 km/h, starting 400 m apart?
(a). 400m
(b). 880m
(c). 1500m
(d). 30km

Answer 1

- Hint: Distance travelled can be found out from the product of speed of the travel and the time spent for that travel. The dog is running until the master and master’s beloved meets. So, the time taken for that meetup can be considered as the time taken by the dog. It can be found from the initial distance between the master and his beloved and the speed of their walking.

Complete step-by-step solution -
It is cleared from the question that the dog ran with a speed of \[30km/h\] from master to master’s beloved and returned to master and so on. They walk for a time until they both meet. So, to find the distance that the dog ran we will use the formula:
$\text{Distance the dog ran = (time taken by amitabh and amrita to meet) }\!\!\times\!\!\text{ (Speed of the dog)}$
So, to find the time taken by amrita and Amitabh to cover a distance of 400 meters, we can use the formula:
$\text{Time taken =}\quad \dfrac{\text{distance between Amitabh and Amrita}}{\text{Total speed}({{V}_{Amitab}}+{{V}_{Amrita}})}$
First, we will convert the speed into meters per hour. For that, we will multiply the given speed by 1000. And then, we will substitute in the above equation.
$\text{Time taken}=\quad \dfrac{400m}{4000\dfrac{m}{h}+4000\dfrac{m}{h}}$
$\text{Time taken}=\dfrac{400}{8000}h$
$\text{Time taken}=0.05h$
Now, we have all the data. We have the speed of the dog and the time until which the dog ran. So, the distance travelled by the dog d
$\text{time taken }\!\!\times\!\!\text{ speed of dog, }d=\quad 0.05h\quad \times \quad 30\dfrac{km}{h}=\quad 1.5km=\quad 1500m$
Therefore, the correct option is c.

Note: Do not forget to change the units from km to m. Sometimes this minor mistake can result in a completely wrong answer. Here the question is asked to find the distance travelled by the dog. So, we can add the distances covered by the dog at that time. If the question is asked to find the displacement, you should consider the least distance between the master and dog. Drunkard problem is also similar to this.