Walking `5/7` of his usual speed, a person reaches his office 10 minutes later than the usual time. His usual time in minutes is :

Options

A. 28
B. 30
C. 25
D. 35

Answer

To solve the problem step by step, we can follow these steps:

### Step 1: Understand the relationship between speed and time
When a person walks at a reduced speed, the time taken to reach a destination increases. The relationship between speed and time can be described as:
- If speed decreases, time increases.

### Step 2: Define the variables
Let:
- Usual speed = \( S \)
- Usual time = \( T \)
- Reduced speed = \( \frac{5}{7}S \)

### Step 3: Establish the time taken at reduced speed
When the person walks at \( \frac{5}{7} \) of his usual speed, the time taken to reach the office becomes:
- New time = \( \frac{T}{\frac{5}{7}} = \frac{7T}{5} \)

### Step 4: Set up the equation based on the information given
According to the problem, the person reaches the office 10 minutes later than usual:
\[ \frac{7T}{5} = T + 10 \]

### Step 5: Solve the equation
To solve for \( T \), we can first eliminate the fraction by multiplying the entire equation by 5:
\[ 7T = 5T + 50 \]
Now, subtract \( 5T \) from both sides:
\[ 2T = 50 \]
Dividing both sides by 2 gives:
\[ T = 25 \]

### Conclusion
The usual time taken by the person to reach his office is **25 minutes**.

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