Speed of ram while travelling from point A to point B is 50 km/hr and while returning he decreased his speed by 40%. Find his average speed of

Options

A. 33.33 km/hr
B. 35.75 km/hr
C. 42.55 km/hr
D. 37.5 km/hr

Answer

To find the average speed of Ram for his journey from point A to point B and back, we can follow these steps:

### Step 1: Determine the speed while going from A to B
Ram's speed while traveling from point A to point B is given as 50 km/hr.

### Step 2: Calculate the speed while returning from B to A
Ram decreases his speed by 40% while returning. To find the new speed:
- Calculate 40% of 50 km/hr:
\[ 40\% \text{ of } 50 = \frac{40}{100} \times 50 = 20 \text{ km/hr} \]
- Subtract this from the original speed:
\[ \text{New speed} = 50 - 20 = 30 \text{ km/hr} \]

### Step 3: Use the average speed formula
The formula for average speed when the distances are the same is:
\[ \text{Average Speed} = \frac{2AB}{A + B} \]
where A is the speed going (50 km/hr) and B is the speed returning (30 km/hr).

### Step 4: Substitute the values into the formula
Substituting A and B into the formula:
\[ \text{Average Speed} = \frac{2 \times 50 \times 30}{50 + 30} \]

### Step 5: Calculate the denominator
Calculate the sum of the speeds:
\[ 50 + 30 = 80 \]

### Step 6: Calculate the numerator
Calculate the product in the numerator:
\[ 2 \times 50 \times 30 = 3000 \]

### Step 7: Final calculation of average speed
Now substitute the values back into the average speed formula:
\[ \text{Average Speed} = \frac{3000}{80} = 37.5 \text{ km/hr} \]

### Conclusion
The average speed of Ram for the entire journey is **37.5 km/hr**.

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