A

We know total distance is 200 Km
If both trains crossed each other at a distance of 110 km then one train covered 110 km and other 90 km [110 + 90 = 200km]
So ratio of their speed = 110:90 = 11:9

C

Let time taken to travel the first half = x hr
Then time taken to travel the second half = (10 – x) hr
Distance covered in the the first half = 21x [because, distance = time [latex]\times[/latex] speed]
Distance covered in the the second half = 24(10 – x)
Distance covered in the the first half = Distance covered in the the second half
So,
21x = 24(10 – x)
[latex]\Rightarrow 45x = 240[/latex]
[latex]\Rightarrow x = \frac {16}{3}[/latex]
Total Distance = [latex]2 \times 21(\frac {16}{3})[/latex] = 224 Km [multiplied by 2 as 21x was distance of half way]

A

Let the time in which he travelled on foot = x hour
Time for travelling on bicycle = (9 – x) hr
Distance = Speed [latex]\times[/latex] Time, and Total distance = 61 km
So,
4x + 9(9-x) = 61
[latex]\Rightarrow[/latex] 5x = 20
[latex]\Rightarrow[/latex] x = 4
So distance traveled on foot = 4(4) = 16 km

C

If the distance be x km, then [latex]\frac {x}{40} -\frac {x}{50} = \frac {6}{60}[/latex]
[latex]\frac {x}{4} - \frac {x}{5} = 1[/latex]
x = 20 km.
Required time = [latex](\frac {20}{40})[/latex] hour – 11 minutes
= [latex](\frac {1}{2} \times 60 - 11)[/latex] minutes = 19 minutes

C

Distance covered in 10 minutes at 20 kmph = distance covered in 8 minutes at (20 + x) kmph
[latex]20 \times \frac {10}{60} = \frac {8}{60(20+x)}[/latex]
200 = 160 + 8x
8x = 40
x = [latex]\frac{40}{8}[/latex] = 5 kmph