Study the following statements carefully and select the correct option.
Statement-I A hall is 36m long and 24m broad. If allowing area of `40m^(2)` for doos and windows, the cost of papering the walls at Rs. 8.40 per square metre is Rs. 4704, then the height of the hall is 5 m.
Statement-II : If the difference between the circumference and diameter of a circle is 154 cm, then the radius of circle is 30.93 cm.

Options

A. Both Statement-I and Statement-II are true.
B. Both Statement-I and Statement-II are false.
C. Statement-I is true but Statement-II is false.
D. Statement-I is false but Statement-II is true.

Answer

To solve the problem step-by-step, we will analyze both statements separately.

### Statement I:
A hall is 36m long and 24m broad. If allowing an area of 40m² for doors and windows, the cost of papering the walls at Rs. 8.40 per square meter is Rs. 4704, then the height of the hall is 5 m.

**Step 1: Calculate the total area of the four walls of the hall.**
The formula for the area of the four walls (excluding the ceiling and floor) is:
\[ \text{Area} = 2 \times \text{height} \times (\text{length} + \text{breadth}) \]

Let the height be \( h \).
Given:
- Length = 36m
- Breadth = 24m

So, the area of the four walls becomes:
\[ \text{Area} = 2 \times h \times (36 + 24) \]
\[ = 2 \times h \times 60 \]
\[ = 120h \]

**Step 2: Subtract the area for doors and windows.**
The area that needs papering is:
\[ \text{Area for papering} = 120h - 40 \]

**Step 3: Calculate the total cost of papering.**
The cost of papering is given as Rs. 4704, and the cost per square meter is Rs. 8.40. Therefore, we can set up the equation:
\[ \text{Cost} = \text{Area for papering} \times \text{Cost per square meter} \]
\[ 4704 = (120h - 40) \times 8.40 \]

**Step 4: Solve for \( h \).**
First, divide both sides by 8.40:
\[ 120h - 40 = \frac{4704}{8.40} \]
Calculating the right side:
\[ 4704 \div 8.40 = 560 \]
So,
\[ 120h - 40 = 560 \]
Now, add 40 to both sides:
\[ 120h = 600 \]
Finally, divide by 120:
\[ h = \frac{600}{120} = 5 \]

**Conclusion for Statement I:**
The height of the hall is indeed 5m, so Statement I is **true**.

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### Statement II:
If the difference between the circumference and diameter of a circle is 154 cm, then the radius of the circle is 30.93 cm.

**Step 1: Write the formulas for circumference and diameter.**
- Circumference \( C = 2\pi r \)
- Diameter \( D = 2r \)

**Step 2: Set up the equation based on the given information.**
The difference between the circumference and diameter is given as:
\[ C - D = 154 \]
Substituting the formulas:
\[ 2\pi r - 2r = 154 \]

**Step 3: Factor out \( 2r \).**
\[ 2r(\pi - 1) = 154 \]

**Step 4: Solve for \( r \).**
First, divide both sides by 2:
\[ r(\pi - 1) = 77 \]
Now, substitute \( \pi \approx \frac{22}{7} \):
\[ r\left(\frac{22}{7} - 1\right) = 77 \]
Calculating \( \frac{22}{7} - 1 = \frac{22 - 7}{7} = \frac{15}{7} \):
\[ r \times \frac{15}{7} = 77 \]

**Step 5: Solve for \( r \).**
Multiply both sides by \( \frac{7}{15} \):
\[ r = 77 \times \frac{7}{15} \]
Calculating:
\[ r = \frac{539}{15} \approx 35.93 \text{ cm} \]

**Conclusion for Statement II:**
The radius of the circle is approximately 35.93 cm, not 30.93 cm, so Statement II is **false**.

### Final Conclusion:
- Statement I is true.
- Statement II is false.