Mrs. Vijaya takes a total of 9 hours 50 minutes in walking a distance and running back to same place where she started. She could walk both ways in 12 hrs 20 minutes. The time taken by her to run both ways is:

Options

A. 7 hours 45 min
B. 7 hours 35 min
C. 7 hours 15 min
D. 7 hours 20 min

Answer

To solve the problem, we need to find the time taken by Mrs. Vijaya to run both ways after knowing the time taken to walk both ways and the total time taken for the entire journey.

### Step-by-step Solution:

1. **Convert the total time into minutes:**
- Total time taken for walking and running = 9 hours 50 minutes.
- Convert this into minutes:
\[ 9 \text{ hours} = 9 \times 60 = 540 \text{ minutes} \]
\[ 540 + 50 = 590 \text{ minutes} \]

2. **Convert the walking time into minutes:**
- Time taken to walk both ways = 12 hours 20 minutes.
- Convert this into minutes:
\[ 12 \text{ hours} = 12 \times 60 = 720 \text{ minutes} \]
\[ 720 + 20 = 740 \text{ minutes} \]

3. **Set up the equation for running time:**
- Let the time taken to run both ways be \( R \) minutes.
- According to the problem, the total time for walking and running is:
\[ \text{Walking time} + \text{Running time} = 590 \text{ minutes} \]
- Since the walking time for both ways is 740 minutes, we can express the equation as:
\[ 740 + R = 590 \]

4. **Solve for the running time \( R \):**
- Rearranging the equation gives:
\[ R = 590 - 740 \]
\[ R = -150 \text{ minutes} \]
- However, this indicates that we need to consider only one way for walking. Since the total walking time is for both ways, we need to divide it by 2.
- So, the walking time for one way is:
\[ \text{Walking time (one way)} = \frac{740}{2} = 370 \text{ minutes} \]
- Now, we can rewrite the equation:
\[ 370 + R = 590 \]
\[ R = 590 - 370 \]
\[ R = 220 \text{ minutes} \]

5. **Calculate the total running time for both ways:**
- Since \( R \) is the time taken for one way, the total running time for both ways is:
\[ \text{Total running time} = 2 \times R = 2 \times 220 = 440 \text{ minutes} \]

6. **Convert the running time back to hours and minutes:**
- To convert 440 minutes back to hours:
\[ 440 \div 60 = 7 \text{ hours} \text{ and } 20 \text{ minutes} \]

### Final Answer:
The time taken by Mrs. Vijaya to run both ways is **7 hours 20 minutes**.

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