Question

Two persons are walking in the same direction at rates 3 km/ hr and 6 km/hr. A train comes running from behind and passes them in 9 and 10 seconds. The speed of the train is

• A. 22 km/hr
• B. 40 km/hr
• C. 33 km/hr
• D. 35 km/hr

Answer 1

The Correct Option is C

Let the speed of the train be \(v\) km/h. 
The relative speed between the train and the first person is \((v - 3)\)km/h.
The train passes the first person in 9 seconds. 

\(\Rightarrow\;\)\(v - 3 \, \text{km/h} = \frac{(v - 3) \times 1000}{3600} \, \text{m/s}\)

Since the train passes the person in 9 seconds, the length of the train can be written as:

\(\Rightarrow\;\)\(\text{Length of train} = (v - 3) \times \frac{1000}{3600} \times 9\)

Similarly, 
the relative speed between the train and the second person is \((v - 6)\) km/h.
The train passes the second person in 10 seconds. 

\(\Rightarrow\;\)\(\text{Length of train} = (v - 6) \times \frac{1000}{3600} \times 10\)

Since the length of the train is the same in both cases, we equate the two equations:

\(\Rightarrow\;\)\((v - 3) \times \frac{1000}{3600} \times 9 = (v - 6) \times \frac{1000}{3600} \times 10\)

\(\Rightarrow\;\)\(9(v - 3) = 10(v - 6)\)

\(\Rightarrow\;\)\(9v - 27 = 10v - 60\)

\(\Rightarrow\;\)\(10v - 9v = 60 - 27\)

\(\Rightarrow\;\)\(v = 33 \, \text{km/h}\)

The correct option is (C): 33 km/hr