A person takes 40 minutes more than his usual time when he covers a distance of 20 km at 5 km/h.If he covers the same distance at 8 km/h, he takes x minutes less than the usual time. Whatis the value of x ?

Options

A. 48
B. 54
C. 45
D. 50

Answer

To solve the problem step by step, we need to find the usual time taken by the person to cover a distance of 20 km, and then calculate how much less time he takes when he increases his speed to 8 km/h.

### Step 1: Calculate the usual time taken at 5 km/h
The formula for time is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
Given:
- Distance = 20 km
- Speed = 5 km/h

Using the formula:
\[ \text{Usual Time} = \frac{20 \text{ km}}{5 \text{ km/h}} = 4 \text{ hours} \]

### Step 2: Determine the time taken at 5 km/h with the additional time
According to the problem, the person takes 40 minutes more than his usual time when traveling at 5 km/h.

Convert 40 minutes to hours:
\[ 40 \text{ minutes} = \frac{40}{60} \text{ hours} = \frac{2}{3} \text{ hours} \]

Thus, the time taken at 5 km/h is:
\[ \text{Time at 5 km/h} = \text{Usual Time} + \frac{2}{3} \text{ hours} = 4 + \frac{2}{3} = \frac{12}{3} + \frac{2}{3} = \frac{14}{3} \text{ hours} \]

### Step 3: Calculate the time taken at 8 km/h
Now, we need to calculate the time taken to cover the same distance of 20 km at a speed of 8 km/h.

Using the formula again:
\[ \text{Time at 8 km/h} = \frac{20 \text{ km}}{8 \text{ km/h}} = 2.5 \text{ hours} \]

### Step 4: Calculate the difference in time from the usual time
Now, we need to find out how much less time he takes at 8 km/h compared to his usual time of 4 hours.

\[ \text{Difference} = \text{Usual Time} - \text{Time at 8 km/h} = 4 \text{ hours} - 2.5 \text{ hours} = 1.5 \text{ hours} \]

### Step 5: Convert the difference into minutes
Convert 1.5 hours to minutes:
\[ 1.5 \text{ hours} = 1.5 \times 60 \text{ minutes} = 90 \text{ minutes} \]

### Conclusion
Thus, the value of \( x \) is:
\[ \boxed{90} \]