Two cars start from Jaipur and Delhi respectively and travel towards each other at a speed of 90 km/h and 80 km/h respectively. By the time they meet, the first car has traveled 180 km more than the second. The distance from Jaipur to Delhi is

Options

A. 3000
B. 3060
C. 3040
D. 3500

Answer

To solve the problem, we need to find the distance between Jaipur and Delhi based on the information given about the two cars.

### Step-by-Step Solution:

1. **Define Variables**:
Let the distance from Jaipur to Delhi be \( D \) km.
The first car (from Jaipur) travels at a speed of 90 km/h and the second car (from Delhi) travels at a speed of 80 km/h.

2. **Distance Traveled by Each Car**:
When the two cars meet, the first car has traveled \( D + 180 \) km and the second car has traveled \( D \) km.

3. **Time Taken by Each Car**:
Since both cars travel for the same amount of time until they meet, we can express the time taken by each car in terms of distance and speed:
- Time taken by the first car:
\[ \text{Time}_1 = \frac{D + 180}{90} \]
- Time taken by the second car:
\[ \text{Time}_2 = \frac{D}{80} \]

4. **Set the Times Equal**:
Since both times are equal, we can set up the equation:
\[ \frac{D + 180}{90} = \frac{D}{80} \]

5. **Cross-Multiply**:
To eliminate the fractions, we cross-multiply:
\[ 80(D + 180) = 90D \]

6. **Expand and Simplify**:
Expanding the left side gives:
\[ 80D + 14400 = 90D \]
Rearranging the equation:
\[ 90D - 80D = 14400 \]
\[ 10D = 14400 \]

7. **Solve for D**:
Dividing both sides by 10:
\[ D = 1440 \text{ km} \]

8. **Total Distance**:
The total distance from Jaipur to Delhi is \( D = 1440 \) km.

### Final Answer:
The distance from Jaipur to Delhi is **1440 km**.