Two persons A and B started from two different places towards each other. If the ratio of their speeds be 3 : 5, then what is the ratio of distance covered by A and B respectively till the point of meeting?

Options

A. `1:2`
B. `3:4`
C. `3:5`
D. `5:3`

Answer

To solve the problem step by step, we will analyze the information given and apply the concept of time, speed, and distance.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- Two persons, A and B, start from two different places and move towards each other.
- The ratio of their speeds is given as 3:5.

2. **Assigning Variables**:
- Let the speed of A be \(3k\) (where \(k\) is a constant).
- Let the speed of B be \(5k\).

3. **Using the Concept of Time**:
- Both A and B will meet at a point after traveling for some time. Since they start at the same time and meet at the same point, the time taken by both to reach the meeting point (let's call it Z) will be the same.
- The formula for time is given by:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

4. **Setting Up the Equation**:
- Let the distance covered by A until they meet be \(X\) and the distance covered by B be \(Y\).
- According to the time formula, we can write:
\[ \frac{X}{3k} = \frac{Y}{5k} \]

5. **Cross Multiplying**:
- To eliminate \(k\) from the equation, we can cross-multiply:
\[ 5kX = 3kY \]
- Dividing both sides by \(k\) (assuming \(k \neq 0\)):
\[ 5X = 3Y \]

6. **Finding the Ratio**:
- Rearranging the equation gives us:
\[ \frac{X}{Y} = \frac{3}{5} \]
- This means the ratio of the distances covered by A and B until they meet is:
\[ \text{Distance covered by A} : \text{Distance covered by B} = 3 : 5 \]

### Final Answer:
The ratio of the distance covered by A and B respectively till the point of meeting is **3 : 5**.

---