Two trains C and D starts moving from stations R and S respectively towards each other. Trains take 4 hours 16 minutes and 3 hours 45 minutes to reach S and R respectively after they meet each other. If the speed of train C is 60 km/hr, then what is the speed of the train D?

Correct option is A

Given:
After meeting:
Train C takes 4 hours 16 minutes to reach station S
Train D takes 3 hours 45 minutes to reach station R
Speed of Train C = 60 km/hr
We need to find the speed of Train D
​
Formula Used:
After meeting, the ratio of speeds is equal to the square root of the inverse ratio of time taken: 

​$$\frac{S_C}{S_D} = \sqrt{\frac{T_D}{T_C}}$$

Calculation:
Convert times into hours:
4 hours 16 minutes = 4 + 16/60 = 64/15 hours
3 hours 45 minutes = 3 + 45/60 = 15/4 hours

Now apply the formula:​​

​$$\frac{60}{S_D} = \sqrt{\frac{15/4}{64/15}} = \sqrt{\frac{15 \times 15}{4 \times 64}} = \sqrt{\frac{225}{256}} = \frac{15}{16}$$

$$\frac{60}{S_D} = \frac{15}{16}$$

$$S_D = \frac{60 \times 16}{15} = \frac{960}{15} = 64 \text{ km/hr}$$​​​​

Final Answer: The speed of Train D is 64 km/hr​