Two trains are running in the same direction with the speeds of 32 km/h and 26 km/h respectively from X and Y. If X is 42 km away from Y and if they meet at a point Z beyond Y, then the distance from Y to Z will be:

Correct option is A

Given:

Speed of Train from X = 32 km/h

Speed of Train from Y = 26 km/h

Distance between X and Y = 42 km

To find: The distance from Y to Z when the trains meet.

Solution:

Since both trains are moving in the same direction, we calculate their relative speed and use it to determine the time taken for them to meet.

Relative speed of the trains (in km/h):

​$$\text{Relative Speed} = 32 - 26 = 6 \, \text{km/h}$$​​

The time taken to meet is given by:

​$$\text{Time to meet} = \frac{\text{Distance between X and Y}}{\text{Relative Speed}} \\\ \\ = \frac{42}{6} = 7 \, \text{hours}$$​​

The distance from Y to Z is calculated using Train 2's speed and the time to meet:

​$$\text{Distance from Y to Z} = \text{Speed of Train from Y} \times \text{Time to meet}\\\ \\ = 26 \times 7 = 182 \, \text{km}$$​​

Therefore, the distance from Y to Z is 182 km.