Priyanka , Akshay and salman started out on a journey to watch the newly released movie "mujhse shaadi Karogi", Which was being shows at wave cine - multiplex. The multiplex was 120km away from their starting point of journey. Priyanka and slman went by car at the speed of 50km/h while akashay travelled by tonga horse cart at 10km/h. After a certain distance salman got off and travelled the rest distance by another Tonga at 10km/h While priyanka went back for Akashay and reached the destination at the same time that salman arrived. the number of hours requried for the trip was:

Options

A. A)4 h
B. B)5 h
C. C)4.8 h
D. D)can't be determined

Answer

To solve the problem step by step, we need to analyze the journey of Priyanka, Akshay, and Salman, and calculate the time taken for their trip.

### Step 1: Understand the Speeds and Distances
- Priyanka and Salman travel by car at a speed of 50 km/h.
- Akshay travels by Tonga horse cart at a speed of 10 km/h.
- The total distance to the multiplex is 120 km.

### Step 2: Define Variables
Let:
- \( V_1 = 10 \) km/h (speed of Akshay)
- \( V_2 = 50 \) km/h (speed of Priyanka and Salman)
- Let \( d \) be the distance traveled by Priyanka and Salman before Salman gets off.

### Step 3: Calculate Time Taken by Each Person
1. **Time taken by Priyanka and Salman to travel distance \( d \)**:
\[ t_1 = \frac{d}{V_2} = \frac{d}{50} \]

2. **Time taken by Akshay to travel distance \( d \)**:
\[ t_2 = \frac{d}{V_1} = \frac{d}{10} \]

### Step 4: Calculate Remaining Distance for Salman
After Salman gets off, he has \( 120 - d \) km left to travel by Tonga at 10 km/h.
- Time taken by Salman to cover the remaining distance:
\[ t_3 = \frac{120 - d}{10} \]

### Step 5: Priyanka's Return Journey
Priyanka goes back to pick up Akshay. The distance she travels back is \( d \) km, and then she travels the remaining distance \( 120 - d \) km to the multiplex.
- Total distance Priyanka travels:
\[ \text{Total distance} = d + (120 - d) = 120 \text{ km} \]
- Time taken by Priyanka to return and reach the multiplex:
\[ t_4 = \frac{d}{50} + \frac{120 - d}{50} = \frac{120}{50} = 2.4 \text{ hours} \]

### Step 6: Set Up the Equation
Since Priyanka and Salman arrive at the same time:
\[ t_1 + t_4 = t_3 \]
Substituting the values:
\[ \frac{d}{50} + 2.4 = \frac{120 - d}{10} \]

### Step 7: Solve for \( d \)
Multiply through by 100 to eliminate the denominators:
\[ 2d + 240 = 1200 - 10d \]
Combine like terms:
\[ 12d = 960 \]
\[ d = 80 \text{ km} \]

### Step 8: Calculate Total Time
Now, we can find the total time taken for the trip:
1. Time for Priyanka and Salman to travel 80 km:
\[ t_1 = \frac{80}{50} = 1.6 \text{ hours} \]
2. Time for Salman to travel the remaining 40 km:
\[ t_3 = \frac{40}{10} = 4 \text{ hours} \]
3. Total time for Priyanka:
\[ t_4 = 2.4 \text{ hours} \]

Adding these times together:
\[ \text{Total time} = t_1 + t_4 = 1.6 + 2.4 = 4 \text{ hours} \]

### Final Answer
The total time required for the trip was **4 hours**.