Sita and Geeta start at the same time to ride from place A to place B, which is 90 km away from A. Sita travels 3 km per hour slower than Geeta. Geeta reaches place B and at once turns back meeting Sita 15 km from place B. Sita's speed (in kmh) is:

Options

A. 9
B. 6
C. 10.5
D. 7.5

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the Variables
Let Geeta's speed be \( x \) km/h. Therefore, Sita's speed will be \( x - 3 \) km/h since Sita travels 3 km/h slower than Geeta.

### Step 2: Calculate the Distances
Geeta travels from A to B (90 km) and then returns back towards Sita until they meet, which is 15 km from B. Therefore, the distance Geeta travels is:
\[ 90 + 15 = 105 \text{ km} \]
Sita, on the other hand, travels from A to the meeting point, which is:
\[ 90 - 15 = 75 \text{ km} \]

### Step 3: Set Up the Time Equation
Since both Sita and Geeta start at the same time and meet at the same time, we can equate the time taken by both to travel their respective distances.

The time taken by Geeta to travel 105 km is:
\[ \text{Time}_{Geeta} = \frac{105}{x} \]

The time taken by Sita to travel 75 km is:
\[ \text{Time}_{Sita} = \frac{75}{x - 3} \]

### Step 4: Set the Times Equal
Since both times are equal:
\[ \frac{105}{x} = \frac{75}{x - 3} \]

### Step 5: Cross-Multiply to Solve for \( x \)
Cross-multiplying gives us:
\[ 105(x - 3) = 75x \]

Expanding this:
\[ 105x - 315 = 75x \]

### Step 6: Rearrange the Equation
Rearranging the equation to isolate \( x \):
\[ 105x - 75x = 315 \]
\[ 30x = 315 \]

### Step 7: Solve for \( x \)
Dividing both sides by 30:
\[ x = \frac{315}{30} = 10.5 \text{ km/h} \]

### Step 8: Find Sita's Speed
Since Sita's speed is \( x - 3 \):
\[ \text{Sita's speed} = 10.5 - 3 = 7.5 \text{ km/h} \]

### Final Answer
Sita's speed is **7.5 km/h**.

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