Anurag started 1 hr late from his home towards his office 140 km away. So, he increased his speed by 40 % and reached office on time. What was the initial speed of Anurag?

Options

A. A)30 km/hr
B. B)40 km/hr
C. C)50 km/hr
D. D)45 km/hr

Answer

To solve the problem, we need to determine Anurag's initial speed based on the information given. Let's break it down step by step.

### Step 1: Understand the Problem
Anurag started 1 hour late and had to travel a distance of 140 km. To make up for the lost time, he increased his speed by 40%.

### Step 2: Define Variables
Let the initial speed of Anurag be \( S \) km/h.

### Step 3: Calculate the Increased Speed
Since Anurag increased his speed by 40%, his new speed becomes:
\[ S_{new} = S + 0.4S = 1.4S \]

### Step 4: Determine the Time Taken at Each Speed
1. **Time taken at initial speed \( S \)**:
\[ \text{Time}_{initial} = \frac{140}{S} \]

2. **Time taken at increased speed \( 1.4S \)**:
\[ \text{Time}_{new} = \frac{140}{1.4S} \]

### Step 5: Set Up the Equation
Since Anurag started 1 hour late, the time taken at the new speed is 1 hour less than the time taken at the initial speed:
\[ \text{Time}_{initial} - \text{Time}_{new} = 1 \]
Substituting the expressions for time:
\[ \frac{140}{S} - \frac{140}{1.4S} = 1 \]

### Step 6: Simplify the Equation
To simplify, find a common denominator:
\[ \frac{140 \cdot 1.4 - 140}{1.4S} = 1 \]
This simplifies to:
\[ \frac{196 - 140}{1.4S} = 1 \]
\[ \frac{56}{1.4S} = 1 \]

### Step 7: Solve for \( S \)
Cross-multiplying gives:
\[ 56 = 1.4S \]
Dividing both sides by 1.4:
\[ S = \frac{56}{1.4} = 40 \]

### Conclusion
The initial speed of Anurag is \( 40 \) km/h.

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