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, we need to find the usual time taken by the person to reach his office. Let's break it down step by step.

### Step 1: Define Variables
Let the usual speed of the person be \( S \) (in units of distance per minute) and the usual time taken to reach the office be \( T \) (in minutes).

### Step 2: Calculate Distance
The distance to the office can be expressed as:
\[ \text{Distance} = \text{Speed} \times \text{Time} = S \times T \]

### Step 3: Determine New Speed
The person walks at \( \frac{5}{7} \) of his usual speed. Therefore, the new speed \( S' \) is:
\[ S' = \frac{5}{7} S \]

### Step 4: Calculate New Time
When walking at the new speed, the time taken to reach the office can be calculated as:
\[ \text{New Time} = \frac{\text{Distance}}{\text{New Speed}} = \frac{S \times T}{\frac{5}{7} S} = \frac{7T}{5} \]

### Step 5: Set Up the Equation
According to the problem, the person reaches his office 10 minutes later than usual when walking at the new speed. Therefore, we can set up the equation:
\[ \text{New Time} - \text{Usual Time} = 10 \]
Substituting the expressions we have:
\[ \frac{7T}{5} - T = 10 \]

### Step 6: Solve for T
To solve for \( T \), we first express \( T \) in terms of a common denominator:
\[ \frac{7T}{5} - \frac{5T}{5} = 10 \]
This simplifies to:
\[ \frac{2T}{5} = 10 \]
Now, multiply both sides by 5:
\[ 2T = 50 \]
Dividing both sides by 2 gives:
\[ T = 25 \]

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