This problem involves calculating the total distance covered by Sohan based on changes in his walking speed and the resulting difference in distance traveled over a fixed time.

Understanding the Problem

We are given the following information:

• Sohan's original travel time to a destination is 15 hours.
• He reduces his walking speed by 1/4th of his original speed.
• As a result of the reduced speed, he travels 5 km less than what he should have actually covered.
• We need to find the total distance covered by Sohan (implicitly, the original distance he could cover in that time).

Step-by-Step Solution

1. Define Variables

Let's denote the variables:

• Original Speed = $S$ km/hr
• Original Time = $T$ = 15 hours
• Original Distance = $D$ km
• Reduced Speed = $S'$
• Distance covered at reduced speed = $D'$

2. Formulate Equations Based on Given Information

We know the relationship between distance, speed, and time is $Distance = Speed \times Time$.

• From the original scenario: $D = S \times T$. Substituting the time, we get: $D = S \times 15$ $D = 15S$ (Equation 1)
• When Sohan reduces his speed by 1/4th, his new speed is: $S' = S - \frac{1}{4}S = \frac{4}{4}S - \frac{1}{4}S = \frac{3}{4}S$
• The distance covered at this reduced speed ($D'$) is 5 km less than the original distance ($D$): $D' = D - 5$
• Assuming he travels for the same duration (15 hours), the distance covered at the reduced speed is: $D' = S' \times T$ $D' = (\frac{3}{4}S) \times 15$ $D' = \frac{45}{4}S$ (Equation 2)

3. Solve for the Original Speed ($S$)

Now we have two expressions for $D'$ (or related to $D$):

• From $D' = D - 5$, substitute $D = 15S$ (from Equation 1): $D' = 15S - 5$
• We also have $D' = \frac{45}{4}S$ (from Equation 2).
• Equating these two expressions for $D'$: $15S - 5 = \frac{45}{4}S$
• To solve for $S$, let's rearrange the equation: $15S - \frac{45}{4}S = 5$
• Find a common denominator (which is 4): $\frac{15 \times 4}{4}S - \frac{45}{4}S = 5$ $\frac{60}{4}S - \frac{45}{4}S = 5$
• Combine the terms: $\frac{60 - 45}{4}S = 5$ $\frac{15}{4}S = 5$
• Isolate $S$: $S = 5 \times \frac{4}{15}$ $S = \frac{20}{15}$ $S = \frac{4}{3}$ km/hr

4. Calculate the Total Distance Covered ($D$)

The question asks for the total distance covered by Sohan. This refers to the distance he would have covered at his original speed in the given time. Using Equation 1:

• $D = 15S$
• Substitute the value of $S$ we found: $D = 15 \times \frac{4}{3}$
• Calculate the distance: $D = \frac{15 \times 4}{3}$ $D = \frac{60}{3}$ $D = 20$ km

5. Verification

Let's check if this distance satisfies the conditions:

• Original Speed $S = \frac{4}{3}$ km/hr. Original Distance $D = 20$ km. Time = $\frac{20 \text{ km}}{4/3 \text{ km/hr}} = 20 \times \frac{3}{4} = 15$ hours. (Matches given time)
• Reduced Speed $S' = \frac{3}{4}S = \frac{3}{4} \times \frac{4}{3} = 1$ km/hr.
• Distance covered at reduced speed in 15 hours = $S' \times 15 = 1 \text{ km/hr} \times 15 \text{ hours} = 15$ km.
• Difference in distance = Original Distance - Reduced Distance = $20 \text{ km} - 15 \text{ km} = 5$ km. (Matches given condition)

Therefore, the total distance covered by Sohan is 20 km.