A man can cover a certain distance in 3 hours 36 minutes if he walks at the rate of 5km/hr. If he covers the same distance on cycle at the rate of 24km/hr, then the time taken by him in minutes is

Options

A. 40
B. 45
C. 50
D. 54

Answer

To solve the problem step by step, we need to find the distance covered by the man when he walks and then calculate the time taken to cover the same distance on a cycle.

### Step 1: Convert the time from hours and minutes to hours only.
The man walks for 3 hours and 36 minutes. We need to convert 36 minutes into hours.

\[ \text{Total time in hours} = 3 + \frac{36}{60} = 3 + 0.6 = 3.6 \text{ hours} \]

### Step 2: Calculate the distance covered while walking.
Using the formula for distance:

\[ \text{Distance} = \text{Speed} \times \text{Time} \]

The speed while walking is 5 km/hr. Therefore, the distance covered is:

\[ \text{Distance} = 5 \text{ km/hr} \times 3.6 \text{ hours} = 18 \text{ km} \]

### Step 3: Calculate the time taken to cover the same distance on a cycle.
Now, we need to find the time taken to cover 18 km at the speed of 24 km/hr. We will use the same distance formula rearranged to find time:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

Substituting the values:

\[ \text{Time} = \frac{18 \text{ km}}{24 \text{ km/hr}} = 0.75 \text{ hours} \]

### Step 4: Convert the time from hours to minutes.
To convert hours into minutes, we multiply by 60:

\[ \text{Time in minutes} = 0.75 \text{ hours} \times 60 = 45 \text{ minutes} \]

### Final Answer:
The time taken by him on the cycle is **45 minutes**.

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