The ratio of speeds of X and y is 5:7. Y covers a distance of 420 km in 3 hours. 'What is the speed of X?

Options

A. 80 kmph
B. 90 kmph
C. 100 kmph
D. 120 kmph

Answer

To solve the problem, we need to find the speed of X given the ratio of speeds of X and Y and the distance covered by Y.

### Step 1: Determine the speed of Y
Y covers a distance of 420 km in 3 hours. We can calculate the speed of Y using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
Substituting the values:
\[ \text{Speed of Y} = \frac{420 \text{ km}}{3 \text{ hours}} = 140 \text{ km/h} \]

### Step 2: Use the ratio of speeds
We know the ratio of speeds of X and Y is 5:7. This means:
\[ \frac{\text{Speed of X}}{\text{Speed of Y}} = \frac{5}{7} \]
Let the speed of X be \(5k\) and the speed of Y be \(7k\).

### Step 3: Set up the equation
Since we have already calculated the speed of Y to be 140 km/h, we can set up the equation:
\[ 7k = 140 \]

### Step 4: Solve for k
To find \(k\), we divide both sides by 7:
\[ k = \frac{140}{7} = 20 \]

### Step 5: Find the speed of X
Now that we have \(k\), we can find the speed of X:
\[ \text{Speed of X} = 5k = 5 \times 20 = 100 \text{ km/h} \]

### Conclusion
The speed of X is **100 km/h**.

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