Each question consists of a question and two statements I and II given below it You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and choose the appropriate option.
What is the value of ‘D’ ?
I. To cover a distance of D km, travelling at 90 kmph, the car would have taken 2 hours 30 minutes less than -the time it took travelling at 60 kmph.
II. Travelling at 45 kmph, the car can cover (D - 90) km in 8 hours.

Options

A. The data in statement I alone are sufficient to answer the question while the data in statement II alone are not sufficient to answerl the question.
B. The data in statement II alone are sufficient to answer the question while the data in statement I alone are not sufficient to answer the question.
C. The data either in statement I alone or in. statement II alone are sufficient to answer the question.
D. The data in both the statements I and II together are not sufficient to answer the question.

Answer

To solve the problem, we need to analyze the two statements provided and determine if they are sufficient to find the value of D.

### Step-by-Step Solution:

**Step 1: Analyze Statement I**

Statement I states:
- To cover a distance of D km, traveling at 90 km/h, the car would have taken 2 hours 30 minutes less than the time it took traveling at 60 km/h.

Let’s denote:
- Time taken at 60 km/h = \( \frac{D}{60} \) hours
- Time taken at 90 km/h = \( \frac{D}{90} \) hours

According to the statement:
\[ \frac{D}{60} - \frac{D}{90} = 2.5 \text{ hours} \]

**Step 2: Solve the Equation from Statement I**

To solve the equation, we first find a common denominator for the left side:
- The common denominator of 60 and 90 is 180.

Rewriting the equation:
\[ \frac{3D}{180} - \frac{2D}{180} = 2.5 \]
\[ \frac{D}{180} = 2.5 \]

Now, multiply both sides by 180:
\[ D = 2.5 \times 180 = 450 \]

Thus, from Statement I, we find \( D = 450 \) km.

**Step 3: Analyze Statement II**

Statement II states:
- Traveling at 45 km/h, the car can cover (D - 90) km in 8 hours.

Using the formula for time:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

We can express this as:
\[ 8 = \frac{D - 90}{45} \]

**Step 4: Solve the Equation from Statement II**

To solve for D, we multiply both sides by 45:
\[ 8 \times 45 = D - 90 \]
\[ 360 = D - 90 \]

Now, add 90 to both sides:
\[ D = 360 + 90 = 450 \]

Thus, from Statement II, we also find \( D = 450 \) km.

### Conclusion

Both statements independently provide sufficient information to determine the value of D. Therefore, the answer is that either statement alone is sufficient to answer the question.

### Final Answer:
The correct option is **3**: Data in either statement I alone or statement II alone are sufficient to answer the question.

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