Each of the following question is followed by two statements I , and II. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.
What is the time taken by Saif to coveca distance: 100 km by car?
I. Saif covers a distance of 100 km in 5 hours using bike.
II. speed of bike and that of car is in ratio 5:7.

Options

A. Only Statement I alone.
B. Only Statement II alone.
C. Both Statements I and II together.
D. Neither Statement I nor II is sufficient.

Answer

To solve the problem of determining the time taken by Saif to cover a distance of 100 km by car, we will analyze the two statements provided and see how they can help us arrive at the answer.

### Step-by-Step Solution:

1. **Understanding the Question**:
We need to find out how long it takes Saif to cover 100 km by car.

2. **Analyzing Statement I**:
- Statement I tells us that Saif covers a distance of 100 km in 5 hours using a bike.
- From this, we can calculate the speed of the bike:
\[ \text{Speed of bike} = \frac{\text{Distance}}{\text{Time}} = \frac{100 \text{ km}}{5 \text{ hours}} = 20 \text{ km/h} \]

3. **Analyzing Statement II**:
- Statement II provides the ratio of the speed of the bike to the speed of the car, which is 5:7.
- This means if the speed of the bike is 5 parts, then the speed of the car is 7 parts.

4. **Finding the Speed of the Car**:
- From Statement I, we found the speed of the bike to be 20 km/h.
- Let’s denote the speed of the bike as \( 5x \) and the speed of the car as \( 7x \).
- Since the speed of the bike is 20 km/h, we can set up the equation:
\[ 5x = 20 \implies x = 4 \]
- Now, we can find the speed of the car:
\[ \text{Speed of car} = 7x = 7 \times 4 = 28 \text{ km/h} \]

5. **Calculating the Time Taken by Car**:
- Now that we have the speed of the car, we can find the time taken to cover 100 km:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{100 \text{ km}}{28 \text{ km/h}} = \frac{100}{28} \text{ hours} \approx 3.57 \text{ hours} \]

6. **Conclusion**:
- Both statements I and II are necessary to find the time taken by Saif to cover 100 km by car. Statement I gives us the speed of the bike, and Statement II provides the ratio needed to find the speed of the car.

### Final Answer:
Both statements I and II together are necessary to answer the question.

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