Kareena and shahid starts from kurla and worli towards worli and kurla respectively at the same time After they meet a shantakruz on the way from kurla to worli, kareena reduces he speed by `33.33%` and returns back to kurla and shahid increase his speed by `33.33%` and returns back to worli. If Kareena takes 2 hours for the entire journey , what is the time taken by shahid for the entire journey?

Options

A. A)96 min
B. B)84 min
C. C)168 min
D. D)can't be determined

Answer

To solve the problem step by step, we will analyze the information given and use it to find the time taken by Shahid for the entire journey.

### Step 1: Understanding the Speeds
- Let Kareena's initial speed be \(3K\) (where \(K\) is a constant).
- After meeting at Shanta Cruz, Kareena reduces her speed by \(33.33\%\), which means her new speed becomes \(2K\).
- Let Shahid's initial speed be \(3S\).
- After meeting, Shahid increases his speed by \(33.33\%\), which means his new speed becomes \(4S\).

**Hint:** Remember that reducing speed by \(33.33\%\) means the new speed is \(66.67\%\) of the original speed, and increasing speed by \(33.33\%\) means the new speed is \(133.33\%\) of the original speed.

### Step 2: Time Taken by Kareena
- We know that Kareena takes a total of \(2\) hours for her entire journey.
- The journey consists of two parts: going to Shanta Cruz and returning back to Kurla.

**Hint:** The total time taken can be divided into the time taken to go to Shanta Cruz and the time taken to return.

### Step 3: Ratio of Speeds and Times
- The ratio of Kareena's speeds while going and returning is \(3K:2K\) or \(3:2\).
- Therefore, the ratio of the time taken by Kareena while going and returning is the inverse, which is \(2:3\).

**Hint:** The time taken is inversely proportional to speed.

### Step 4: Calculating Time Taken by Kareena
- Let the time taken to go to Shanta Cruz be \(2x\) and the time taken to return be \(3x\).
- According to the total time given, \(2x + 3x = 2\) hours.
- This simplifies to \(5x = 2\) hours, so \(x = \frac{2}{5}\) hours.
- Therefore, the time taken to go to Shanta Cruz is \(2x = \frac{4}{5}\) hours (or \(48\) minutes) and the time taken to return is \(3x = \frac{6}{5}\) hours (or \(72\) minutes).

**Hint:** Convert hours to minutes for easier calculation.

### Step 5: Time Taken by Shahid
- The ratio of Shahid's speeds while going and returning is \(3S:4S\) or \(3:4\).
- Therefore, the ratio of the time taken by Shahid while going and returning is \(4:3\).
- Let the time taken by Shahid to go to Shanta Cruz be \(4y\) and the time taken to return be \(3y\).
- The total time taken by Shahid is \(4y + 3y = 7y\).

**Hint:** Use the same method of ratios to find the time for Shahid.

### Step 6: Relating Shahid's Time to Kareena's Time
- Since we know Kareena took \(48\) minutes to go, we can set up the equation:
- \(4y = 48\) minutes.
- Solving for \(y\), we find \(y = 12\) minutes.
- Therefore, the total time taken by Shahid is \(7y = 7 \times 12 = 84\) minutes.

**Hint:** Make sure to add both parts of the journey for Shahid to get the total time.

### Final Answer
Shahid takes **84 minutes** for the entire journey.