Two boats X and Y start towards each other from two different places, 300 km apart. The speed of the boat X and Y in still water are 8 km/hr and 7 km/hr respectively. If X proceeds down and Y up the stream, they will meet after.

The correct option is 20 hours.

Step-by-step Explanation:

1. Understand the given data:

• Distance between two places = 300 km

• Speed of boat X in still water = 8 km/hr

• Speed of boat Y in still water = 7 km/hr

• Boat X is moving downstream (with the stream current).

• Boat Y is moving upstream (against the stream current).

2. Calculate effective speeds of both boats:

Let the speed of the stream be $v$ km/hr.

Since boat X proceeds downstream:

$\text{Speed of boat X}=(8+v)\text{km/hr}$

Since boat Y proceeds upstream:

$\text{Speed of boat Y}=(7-v)\text{km/hr}$

3. Calculate relative speed when moving towards each other:

When two objects move towards each other, their relative speed is the sum of their individual speeds.

$\text{Relative Speed}=\text{Speed of boat X}+\text{Speed of boat Y}$

$\text{Relative Speed}=(8+v)+(7-v)$

$\text{Relative Speed}=8+7+v-v=15\text{km/hr}$

Notice that the speed of the stream ($v$) cancels out completely!

4. Calculate the meeting time:

Using the time formula:

$\text{Time}=\frac{\text{Distance}}{\text{Relative Speed}}$

$\text{Time}=\frac{300\text{km}}{15\text{km/hr}}=20\text{hours}$

Therefore, boats X and Y will meet after 20 hours.