A train approaches a tunnel MN. A dog is inside the tunnel at 2/5 the distance from the entrance M. If it runs towards M, the train catches it exactly at M. If it runs towards N, the train catches it exactly at N. Find the ratio of the dog’s speed to the train’s speed.
एक ट्रेन सुरंग MN की ओर आ रही है। एक कुत्ता सुरंग के अंदर, एंट्रेंस M से 2/5 दूरी पर है। अगर वह M की ओर दौड़ता है, तो ट्रेन उसे ठीक M पर पकड़ लेती है। अगर वह N की ओर दौड़ता है, तो ट्रेन उसे ठीक N पर पकड़ लेती है। कुत्ते की स्पीड और ट्रेन की स्पीड का अनुपात ज्ञात करें।
Given:
A train approaches a tunnel MN. A dog is inside the tunnel at a point located at a distance of 2/5 of the total length of the tunnel from the entrance M.
When the train whistles, the dog runs.
• If the dog runs towards M, the train catches the dog exactly at M.
• If the dog runs towards N, the train catches the dog exactly at N.
Calculations:
Let the length of the tunnel be x.
Let the distance of the train from entrance M be y.
Let the speeds of the train and dog be t and d respectively.
When the dog runs 2x/5 towards M, the train covers distance y.
(2x/5) / d = y / t ...(i)
When the dog runs 3x/5 towards N, the train covers distance (x + y).
(3x/5) / d = (x + y) / t ...(ii)
Taking ratio of (ii) to (i):
3/2 = (x + y) / y
3y = 2x + 2y
y = 2x ...(iii)
Substituting (iii) in (i):
(2x/5) / d = 2x / t
t = 5d
∴ The ratio of the speed of the dog and the train is 1 : 5