Hema takes a total of 9 hours 55 min to walk a certain in distance and then cycling back to tile same place
from where she had started. She could walk both ways in 12 hours 30 min. The time she will take to cycle both ways is

Options

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

Answer

To solve the problem step by step, we will break down the information provided and calculate the required time for Hema to cycle both ways.

### Step 1: Convert all time into minutes
First, we need to convert the time Hema takes into minutes for easier calculations.

- Total time taken for walking and cycling (one way) = 9 hours 55 minutes
- Convert to minutes:
\[ 9 \times 60 + 55 = 540 + 55 = 595 \text{ minutes} \]

- Total time taken for walking both ways = 12 hours 30 minutes
- Convert to minutes:
\[ 12 \times 60 + 30 = 720 + 30 = 750 \text{ minutes} \]

### Step 2: Calculate the time taken to walk one way
Since the total time for walking both ways is 750 minutes, the time taken to walk one way is:
\[ \text{Time for one way walking} = \frac{750}{2} = 375 \text{ minutes} \]

### Step 3: Calculate the time taken to cycle one way
Now, we know the total time for walking and cycling one way is 595 minutes. We can find the time taken to cycle one way by subtracting the time taken to walk one way from the total time:
\[ \text{Time for one way cycling} = 595 - 375 = 220 \text{ minutes} \]

### Step 4: Calculate the time taken to cycle both ways
To find the total time taken to cycle both ways, we multiply the time taken to cycle one way by 2:
\[ \text{Time for both ways cycling} = 220 \times 2 = 440 \text{ minutes} \]

### Step 5: Convert the total cycling time back to hours and minutes
Now, we convert 440 minutes back into hours and minutes:
\[ 440 \div 60 = 7 \text{ hours} \quad \text{(with a remainder of } 20 \text{ minutes)} \]
Thus, the total time taken to cycle both ways is:
\[ 7 \text{ hours } 20 \text{ minutes} \]

### Final Answer
Hema will take **7 hours 20 minutes** to cycle both ways.

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