Vikash and Mohit started from point A towards point Q. Distance between A and Q is 9 km. If Mohit starts after 4 min., then he will meet Vikash 1 km away from point Q at a time when Vikash is returning towards point A after reaching point Q and Vikash can cover 1 km in 6 min. find speed of Mohit in km/min.

Options

A. `(1)/(7)`
B. `(1)/(8)`
C. `(1)/(9)`
D. `(1)/(6)`

Answer

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

### Step 1: Understand the scenario
Vikash and Mohit start from point A towards point Q, which is 9 km away. Vikash starts first, and Mohit starts 4 minutes later. They meet 1 km away from point Q, meaning Vikash has traveled 8 km when they meet.

**Hint:** Visualize the problem by sketching the points A and Q, and the meeting point.

### Step 2: Calculate the total distance Vikash travels
When they meet, Vikash has traveled from A to Q and then 1 km back towards A. Therefore, the total distance Vikash travels is:
- Distance from A to Q = 9 km
- Distance from Q back towards A = 1 km
- Total distance = 9 km + 1 km = 10 km

**Hint:** Remember to add the distance Vikash travels after reaching Q.

### Step 3: Calculate the time taken by Vikash
Vikash covers 1 km in 6 minutes. Therefore, the time taken to cover 10 km is:
- Time for 1 km = 6 minutes
- Time for 10 km = 10 km × 6 minutes/km = 60 minutes

**Hint:** Use the formula: Time = Distance × Time per unit distance.

### Step 4: Calculate the time Mohit travels
Since Mohit starts 4 minutes after Vikash, the time Mohit has been traveling when they meet is:
- Time taken by Vikash = 60 minutes
- Time taken by Mohit = 60 minutes - 4 minutes = 56 minutes

**Hint:** Subtract the delay time from Vikash's total time.

### Step 5: Calculate the distance Mohit travels
When they meet, Vikash has traveled 8 km (since he is 1 km away from Q). Mohit must also have traveled the same distance of 8 km when they meet.

**Hint:** Recognize that they meet at the same point, so their distances must be equal at that moment.

### Step 6: Calculate the speed of Mohit
Speed is calculated using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
For Mohit:
- Distance = 8 km
- Time = 56 minutes

Thus, Mohit's speed is:
\[ \text{Speed} = \frac{8 \text{ km}}{56 \text{ min}} = \frac{1}{7} \text{ km/min} \]

**Hint:** Simplify the fraction to find the speed.

### Final Answer
The speed of Mohit is \( \frac{1}{7} \) km/min.

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