Shatabdi Express leaves Patna at 8:00 am for Delhi. At what time will it reach Delhi?
Statements:
For the first 100 km it travels at the, speed of 250 km per hour and maintains the same speed during the entire journey.
It has 5 stoppages between Delhi and Patna
Before every stoppage, it covers a same distance of 240 km.

Options

A. Data in either statement III alone or statements I and II together are sufficient to answer the question
B. Data is only statement III is sufficient to answer the question
C. Data is only statement I and II together are sufficient to answer the question
D. Data is all statement I, II and III together are sufficient to answer the question

Answer

To solve the problem step by step, we need to determine the total distance the Shatabdi Express travels from Patna to Delhi, the speed at which it travels, and then calculate the time taken for the journey. Finally, we will add this time to the departure time to find the arrival time in Delhi.

### Step 1: Determine the Total Distance
The train has 5 stoppages, and before each stoppage, it covers a distance of 240 km. Since there are 5 stoppages, it will cover this distance before each stoppage plus the distance to the final destination.

- Distance before each stoppage = 240 km
- Total distance covered before stoppages = 240 km × 5 = 1200 km
- Distance to the final destination (after the last stoppage) = 240 km

Thus, the total distance from Patna to Delhi is:
\[ \text{Total Distance} = 1200 \text{ km} + 240 \text{ km} = 1440 \text{ km} \]

### Step 2: Determine the Speed
The train travels at a constant speed of 250 km/h throughout the journey.

### Step 3: Calculate the Time Taken
We can use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

Substituting the values we have:
\[ \text{Time} = \frac{1440 \text{ km}}{250 \text{ km/h}} \]

Calculating this gives:
\[ \text{Time} = 5.76 \text{ hours} \]

### Step 4: Convert Time to Hours and Minutes
To convert 0.76 hours into minutes:
\[ 0.76 \text{ hours} \times 60 \text{ minutes/hour} = 45.6 \text{ minutes} \approx 46 \text{ minutes} \]

Thus, the total time taken for the journey is approximately 5 hours and 46 minutes.

### Step 5: Calculate the Arrival Time
The train leaves Patna at 8:00 AM. Adding the travel time to this departure time:
- Departure time: 8:00 AM
- Travel time: 5 hours 46 minutes

Adding these together:
- 8:00 AM + 5 hours = 1:00 PM
- 1:00 PM + 46 minutes = 1:46 PM

Thus, the train will reach Delhi at approximately **1:46 PM**.

### Summary of Steps:
1. Calculate the total distance covered before each stoppage and to the final destination.
2. Use the speed of the train to calculate the total time taken for the journey.
3. Convert the time taken into hours and minutes.
4. Add the travel time to the departure time to find the arrival time.