The ratio of the speeds of A and B is 2 : 5. To cover a certain distance, if A takes 15 minutes more than B, then how much time (in minutes) will B take to cover the same distance?

Options

A. 12
B. 8
C. 10
D. 9

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the Speed Ratio
The ratio of the speeds of A and B is given as 2:5. This means that if A's speed is 2 units, then B's speed is 5 units.

**Hint:** Remember that speed is inversely proportional to time when covering the same distance.

### Step 2: Establish the Time Ratio
Since speed and time are inversely related, the ratio of their times will be the inverse of the speed ratio. Therefore, the time ratio of A to B will be 5:2.

**Hint:** If the speed ratio is a:b, then the time ratio will be b:a.

### Step 3: Assign Variables for Time
Let the time taken by B to cover the distance be \(2x\) minutes. Consequently, the time taken by A will be \(5x\) minutes.

**Hint:** Use variables to represent unknown quantities to make calculations easier.

### Step 4: Set Up the Equation
According to the problem, A takes 15 minutes more than B. Therefore, we can set up the equation:
\[ 5x = 2x + 15 \]

**Hint:** This equation represents the relationship between the times taken by A and B.

### Step 5: Solve for x
Now, we will solve the equation:
\[ 5x - 2x = 15 \\ 3x = 15 \\ x = 5 \]

**Hint:** Isolate the variable to find its value.

### Step 6: Calculate B's Time
Now that we have the value of \(x\), we can find the time taken by B:
\[ \text{Time taken by B} = 2x = 2 \times 5 = 10 \text{ minutes} \]

**Hint:** Substitute the value of \(x\) back into the expression for B's time.

### Conclusion
B takes 10 minutes to cover the same distance.

**Final Answer:** 10 minutes