By walking at `3/4` of his usual speed, a man reaches his office 20 minutes later than his usual time. The usual time taken by him to reach his office is

Options

A. 75 minutes
B. 60 minutes
C. 40 minutes
D. 30 minutes

Answer

To solve the problem step by step, we will denote the usual time taken by the man to reach his office as \( x \) minutes.

### Step 1: Understand the relationship between speed and time
When the man walks at \( \frac{3}{4} \) of his usual speed, the time taken to reach his office increases. The relationship between speed and time is inversely proportional; thus, if speed decreases, time increases.

### Step 2: Express the new time taken
If the man's usual speed is \( S \), then his usual time taken to reach the office is \( x \) minutes. When he walks at \( \frac{3}{4} S \), the time taken becomes:
\[ \text{New time} = \frac{\text{Usual time}}{\text{Fraction of speed}} = \frac{x}{\frac{3}{4}} = \frac{4x}{3} \]

### Step 3: Set up the equation based on the problem statement
According to the problem, the man reaches his office 20 minutes later than usual when walking at \( \frac{3}{4} S \). Therefore, we can set up the equation:
\[ \frac{4x}{3} - x = 20 \]

### Step 4: Simplify the equation
To simplify the left side:
\[ \frac{4x}{3} - \frac{3x}{3} = \frac{4x - 3x}{3} = \frac{x}{3} \]
So, the equation becomes:
\[ \frac{x}{3} = 20 \]

### Step 5: Solve for \( x \)
To find \( x \), multiply both sides by 3:
\[ x = 20 \times 3 = 60 \]

### Conclusion
The usual time taken by the man to reach his office is \( 60 \) minutes.