Babu generally starts from his home at certain time with a certain speed to pick up his girlfriend from office at 5:00 PM. One day his girlfriend left the office at 3:00 PM and starts walking to home with a speed of 40 km/hr and meet Babu in the way who left his home at his usual time. They reached home 40 min. Earlier than their usual time.
Quantity I: Speed of boy.
Quantity II: speed of girl.

Options

A. Quantity I ` gt` Quantity II
B. Quantity I `lt` Quantity II
C. Quantity I `ge `Quantity II
D. Quantity I `le` QuantityII

Answer

To solve the problem step by step, we need to analyze the situation involving Babu and his girlfriend.

### Step 1: Understand the scenario
Babu usually leaves his home at a certain time to pick up his girlfriend from her office at 5:00 PM. On this particular day, his girlfriend leaves the office at 3:00 PM and starts walking home at a speed of 40 km/hr. They meet on the way and arrive home 40 minutes earlier than usual.

**Hint:** Identify the key times and speeds involved in the scenario.

### Step 2: Determine the time saved
Since they reached home 40 minutes earlier than usual, we can infer that the total time saved is due to the girlfriend walking towards home. Babu saves time by not having to go all the way to the office.

**Hint:** Calculate how much time they saved in terms of minutes.

### Step 3: Calculate the time of meeting
Babu would typically leave home at a time that allows him to arrive at the office by 5:00 PM. Since they saved 40 minutes, they must have reached home at 4:20 PM. This means Babu must have met his girlfriend at 4:00 PM.

**Hint:** Establish the time when they met based on the total time saved.

### Step 4: Determine how long the girlfriend walked
The girlfriend started walking at 3:00 PM and met Babu at 4:00 PM. Therefore, she walked for 1 hour (from 3:00 PM to 4:00 PM) at a speed of 40 km/hr.

**Hint:** Use the formula Distance = Speed × Time to find out how far the girlfriend walked.

### Step 5: Calculate the distance the girlfriend covered
Distance covered by the girlfriend = Speed × Time = 40 km/hr × 1 hr = 40 km.

**Hint:** This distance is crucial as it helps us find out how far Babu had to travel.

### Step 6: Determine the distance Babu traveled
Since the girlfriend walked 40 km towards home, Babu must have traveled the remaining distance to meet her. If he usually takes the same route, we can assume he would have traveled the same distance.

**Hint:** Consider the total distance from Babu's home to the office and how it relates to the distance the girlfriend walked.

### Step 7: Establish the time taken by Babu
If Babu met his girlfriend at 4:00 PM and they saved 40 minutes, we can deduce that he would have normally arrived at home at 5:00 PM. Therefore, he must have left home at 4:00 PM to meet her.

**Hint:** Calculate the time taken by Babu to reach the meeting point.

### Step 8: Calculate Babu's speed
Let’s assume the distance from Babu's home to the meeting point is also 40 km. If Babu took 20 minutes to reach the meeting point (since they saved 40 minutes total, and 20 minutes is saved on each leg of the trip), we can calculate his speed.

Time taken = 20 minutes = 1/3 hour.
Distance = 40 km.

Speed of Babu = Distance / Time = 40 km / (1/3 hr) = 40 km × 3 = 120 km/hr.

**Hint:** Use the formula Speed = Distance / Time to find Babu's speed.

### Step 9: Compare the speeds
Now we have:
- Speed of Babu = 120 km/hr
- Speed of girlfriend = 40 km/hr

**Hint:** Compare the two quantities to determine which is greater.

### Conclusion
Quantity I (Speed of Babu) is 120 km/hr, and Quantity II (Speed of girlfriend) is 40 km/hr. Therefore, Quantity I is greater than Quantity II.

**Final Answer:** Quantity I is greater than Quantity II.