Two trains start at the same time from points A and B towards each other and after crossing each other, they take 25 h and 9 h in reaching points B and A, respectively. Find the ratio of speeds of 1st train to that of 2nd train.

Answer

To find the ratio of the speeds of the first train to the second train, we can use the relationship between the time taken by each train after they cross each other and their speeds.

Let's denote:
- Speed of the first train = S1
- Speed of the second train = S2
- Time taken by the first train to reach point B after crossing = T1 = 25 hours
- Time taken by the second train to reach point A after crossing = T2 = 9 hours

### Step 1: Establish the relationship between speeds and times
When two trains cross each other, the distance each train travels after crossing is proportional to their speeds. Therefore, we can write:

\[ \frac{S1}{S2} = \frac{T2}{T1} \]

### Step 2: Substitute the values of T1 and T2
Now, substituting the values of T1 and T2 into the equation:

\[ \frac{S1}{S2} = \frac{9}{25} \]

### Step 3: Simplify the ratio
This gives us the ratio of the speeds of the first train to the second train:

\[ S1 : S2 = 9 : 25 \]

### Conclusion
Thus, the ratio of the speeds of the first train to the second train is:

\[ \boxed{9 : 25} \]