Manish goes to his hometown at the speed of 40 km/hr and returns to his home at the speed of Y km/hr. Distance between his home and hometown is 360 km. If he takes total 21 hours, then what is the value of Y?

Options

A. A) 25 km/hr
B. B) 28 km/hr
C. C) 30 km/hr
D. D) 33 km/hr

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the Given Information
- Distance from home to hometown = 360 km
- Speed while going to hometown = 40 km/hr
- Total time taken for the round trip = 21 hours
- Speed while returning = Y km/hr (which we need to find)

### Step 2: Calculate Time Taken to Go to Hometown
The time taken to go to the hometown can be calculated using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
Substituting the known values:
\[ \text{Time for going} = \frac{360 \text{ km}}{40 \text{ km/hr}} = 9 \text{ hours} \]

### Step 3: Calculate Time Taken to Return
Since the total time for the round trip is 21 hours, we can find the time taken to return by subtracting the time taken to go from the total time:
\[ \text{Time for returning} = 21 \text{ hours} - 9 \text{ hours} = 12 \text{ hours} \]

### Step 4: Calculate the Speed While Returning
Now, we can find the speed while returning (Y) using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
Substituting the known values for the return trip:
\[ Y = \frac{360 \text{ km}}{12 \text{ hours}} = 30 \text{ km/hr} \]

### Conclusion
Thus, the speed while returning (Y) is:
\[ Y = 30 \text{ km/hr} \]