A man goes to a place at a speed of 80 km/hr and comes back with a different speed. If the average speed is 32 km/hr, then what is the return speed (in km/hr)?

Options

A. 25
B. 22
C. 20
D. 24

Answer

To solve the problem step by step, we can use the formula for average speed when the distance is the same for both parts of the journey. The formula for average speed when traveling to and from a place is given by:

\[ \text{Average Speed} = \frac{2xy}{x + y} \]

Where:
- \(x\) is the speed going to the destination (80 km/hr),
- \(y\) is the speed coming back (unknown),
- The average speed is given as 32 km/hr.

### Step 1: Set up the equation using the average speed formula

Substituting the known values into the formula:

\[ 32 = \frac{2 \cdot 80 \cdot y}{80 + y} \]

### Step 2: Simplify the equation

Multiply both sides by \(80 + y\) to eliminate the fraction:

\[ 32(80 + y) = 160y \]

### Step 3: Distribute the left side

Distributing \(32\) gives:

\[ 2560 + 32y = 160y \]

### Step 4: Rearrange the equation

Now, rearranging the equation to isolate \(y\):

\[ 2560 = 160y - 32y \]
\[ 2560 = 128y \]

### Step 5: Solve for \(y\)

Now, divide both sides by \(128\):

\[ y = \frac{2560}{128} \]
\[ y = 20 \]

### Conclusion

The return speed \(y\) is \(20\) km/hr.

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