Ashok and Sarvesh start walking towards each other at 8 : 20 hrs in moring from A and B respectively. Ratio of their speed is 4 : 5. They meet at point C at a certain time and hav snacks together. At 9 : 27 am they again start walking towards their destination. If Ashok reach at B on 10 : 32 am, how much time they spent together ?

Options

A. a)8 min
B. b)12 min
C. c)15 min
D. d)Cannot be calculated

Answer

To solve the problem step by step, we will analyze the information given and calculate the time Ashok and Sarvesh spent together.

### Step 1: Understand the Problem
Ashok and Sarvesh start walking towards each other at 8:20 AM. The ratio of their speeds is 4:5. They meet at point C and have snacks together before continuing to their destinations.

### Step 2: Determine Meeting Time
They meet at point C and then start walking again at 9:27 AM. We need to find out how long they spent together after meeting.

### Step 3: Calculate Ashok's Travel Time
Ashok reaches point B at 10:32 AM. We can calculate the total travel time for Ashok from 8:20 AM to 10:32 AM.

- Start time: 8:20 AM
- End time: 10:32 AM

Total travel time for Ashok:
- From 8:20 AM to 9:27 AM = 1 hour 7 minutes (67 minutes)
- From 9:27 AM to 10:32 AM = 1 hour 5 minutes (65 minutes)

Total time Ashok traveled = 67 minutes + 65 minutes = 132 minutes.

### Step 4: Calculate Distance Ratios
Since the ratio of their speeds is 4:5, we can assign distances based on this ratio. Let the distance Ashok travels to point C be 4X and the distance Sarvesh travels to point C be 5X.

### Step 5: Calculate Time Taken to Travel Distances
From the total time Ashok traveled (132 minutes), we can determine how long it took him to travel each segment.

- The time taken by Ashok to travel distance 5X (from C to B) is 65 minutes.
- Therefore, the time taken to travel distance 4X (from A to C) is:
\[ \text{Time for 4X} = 132 \text{ minutes} - 65 \text{ minutes} = 67 \text{ minutes} \]

### Step 6: Determine Time Spent Together
Now, we need to find out how long they spent together after meeting at point C. They started walking again at 9:27 AM, and Ashok took 65 minutes to reach B from C.

- Since they met at point C and Ashok took 65 minutes to reach B, they spent the time from when they met until Ashok left for B.
- Ashok left at 9:27 AM and took 65 minutes to reach B, which means he arrived at B at 10:32 AM.

### Step 7: Calculate Total Time Spent Together
The time they spent together after meeting until Ashok left at 9:27 AM is:
- They met at some time before 9:27 AM, and since Ashok took 67 minutes to travel from A to C, they spent:
\[ \text{Time spent together} = 9:27 \text{ AM} - (8:20 \text{ AM} + 67 \text{ minutes}) \]

Calculating the time:
- 8:20 AM + 67 minutes = 9:27 AM (which is when they started walking again).

Thus, they spent **15 minutes** together.

### Final Answer
The time they spent together is **15 minutes**.