Monal Kumar travelled equal distance with speed of 3 km/hr, 5 km/hr and 8 km/hr and takes a total time of 39.5 minutes. Find the total distance in km.
A. 4
B. 2
C. 1
D. 3

Options

A. D
B. A
C. C
D. D

Answer

To solve the problem step by step, we need to find the total distance Monal Kumar traveled given that he traveled equal distances at different speeds and took a total time of 39.5 minutes.

### Step 1: Define the distance
Let the distance traveled at each speed be \( x \) km.

### Step 2: Calculate the time taken for each speed
- Time taken at 3 km/hr:
\[ t_1 = \frac{x}{3} \text{ hours} \]
- Time taken at 5 km/hr:
\[ t_2 = \frac{x}{5} \text{ hours} \]
- Time taken at 8 km/hr:
\[ t_3 = \frac{x}{8} \text{ hours} \]

### Step 3: Total time in hours
The total time taken is given as 39.5 minutes. We need to convert this into hours:
\[ 39.5 \text{ minutes} = \frac{39.5}{60} \text{ hours} \]

### Step 4: Set up the equation for total time
The total time can be expressed as:
\[ t_1 + t_2 + t_3 = \frac{39.5}{60} \]
Substituting the expressions for \( t_1, t_2, \) and \( t_3 \):
\[ \frac{x}{3} + \frac{x}{5} + \frac{x}{8} = \frac{39.5}{60} \]

### Step 5: Find a common denominator
The least common multiple (LCM) of 3, 5, and 8 is 120. We can rewrite the left side:
\[ \frac{40x}{120} + \frac{24x}{120} + \frac{15x}{120} = \frac{39.5}{60} \]
Combining the fractions:
\[ \frac{(40 + 24 + 15)x}{120} = \frac{39.5}{60} \]
This simplifies to:
\[ \frac{79x}{120} = \frac{39.5}{60} \]

### Step 6: Cross-multiply to solve for \( x \)
Cross-multiplying gives:
\[ 79x \times 60 = 39.5 \times 120 \]
Calculating the right side:
\[ 39.5 \times 120 = 4740 \]
So we have:
\[ 4740 = 79x \times 60 \]

### Step 7: Isolate \( x \)
Now, divide both sides by 79:
\[ x = \frac{4740}{79 \times 60} \]
Calculating \( 79 \times 60 = 4740 \):
\[ x = \frac{4740}{4740} = 1 \]

### Step 8: Calculate total distance
Since Monal traveled the same distance \( x \) at three different speeds, the total distance traveled is:
\[ \text{Total Distance} = 3x = 3 \times 1 = 3 \text{ km} \]

### Final Answer
The total distance Monal Kumar traveled is **3 km**. Thus, the correct option is **D. 3**.

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