Ashok reach 6 min. late when travelling with speed of 60 km./hr. to city. He increases his speed by 20 km./hr. on next day and reach 4 min. before-
(i) Find distance between house and city ?
(ii) Time taken to reach city. Calculate ?
(iii) If he want to reach on time, at what speed he has to travel ?

Options

A. 40 km., 34 minute, `70 (10)/(17)` km./hr.
B. 80 km., 60 minute, `70 (10)/(17)` km./hr.
C. 55 km., 45 minute, `68 (10)/(17)` km./hr.
D. None of these

Answer

To solve the problem step by step, we will use the relationships between speed, time, and distance. Let's break it down:

### Step 1: Define Variables
Let the normal time taken to reach the city be \( x \) minutes.

### Step 2: Set Up Equations
1. When Ashok travels at 60 km/hr, he is 6 minutes late. Therefore, the time taken is:
\[ t_1 = x + 6 \text{ minutes} \]
2. When he increases his speed to 80 km/hr (60 km/hr + 20 km/hr), he arrives 4 minutes early. Therefore, the time taken is:
\[ t_2 = x - 4 \text{ minutes} \]

### Step 3: Distance Equation
Since the distance remains constant, we can set up the equation based on the formula \( \text{Distance} = \text{Speed} \times \text{Time} \):
\[ \text{Distance} = 60 \times (x + 6) = 80 \times (x - 4) \]

### Step 4: Expand and Simplify
Expanding both sides:
\[ 60x + 360 = 80x - 320 \]

### Step 5: Rearranging the Equation
Rearranging gives:
\[ 360 + 320 = 80x - 60x \]
\[ 680 = 20x \]

### Step 6: Solve for \( x \)
Dividing both sides by 20:
\[ x = \frac{680}{20} = 34 \text{ minutes} \]

### Step 7: Calculate the Distance
Now that we have \( x \), we can calculate the distance:
Using the first speed:
\[ \text{Distance} = 60 \times (34 + 6) = 60 \times 40 = 2400 \text{ km} \]

### Step 8: Time Taken to Reach City
The time taken to reach the city is \( x = 34 \) minutes.

### Step 9: Calculate Speed to Reach on Time
If Ashok wants to reach on time, he needs to travel the distance at the normal time:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{2400 \text{ km}}{\frac{34}{60} \text{ hr}} = \frac{2400 \text{ km}}{0.5667 \text{ hr}} \approx 4236 \text{ km/hr} \]

### Final Answers
1. The distance between Ashok's house and the city is **2400 km**.
2. The time taken to reach the city is **34 minutes**.
3. The speed he needs to travel to reach on time is approximately **4236 km/hr**.