The following questions are accompanied by two statements (I) and (II). You have to determine which statements(s) is/are sufficient/ necessary to answer the questions.
Find value of R.
I. Sameer invested Rs.5000 each at R% p.a. SI and R% p.a. Ci respectively for 2 years. Total compound interest received is Rs. 112.5 more than total simple interest received by him,
II. Anurag invested Rs.X at R% p.a. at SI for 2 years and Rs.4000 at (R+5)% p.a. at SI for 3 years. Total interest received by him is Rs.4200.

Options

A. Statement (I) alone is sufficient to answer the question but statement (II) alone is not sufficient to answer the question
B. Statement (II) alone is sufficient to answer the question but statement (I) alone is not sufficient to answer the question.
C. Both the statements taken together are necessary to answer the question, but neither of the statements alone is sufficient to answer the question.
D. Either statement (I) or statement (II) by itself is 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 R.

### Step-by-Step Solution:

**Step 1: Analyze Statement I**

Statement I states:
"Sameer invested Rs.5000 each at R% p.a. SI and R% p.a. CI respectively for 2 years. Total compound interest received is Rs. 112.5 more than total simple interest received by him."

1. **Calculate Simple Interest (SI):**
- Formula for Simple Interest:
\[ SI = \frac{P \times R \times T}{100} \]
- Here, \( P = 5000 \), \( R = R \), and \( T = 2 \).
- Thus,
\[ SI = \frac{5000 \times R \times 2}{100} = 100R \]

2. **Calculate Compound Interest (CI):**
- Formula for Compound Interest:
\[ CI = P \left(1 + \frac{R}{100}\right)^T - P \]
- Here, substituting the values:
\[ CI = 5000 \left(1 + \frac{R}{100}\right)^2 - 5000 \]

3. **Set up the equation based on the information given:**
- According to the statement,
\[ CI = SI + 112.5 \]
- Therefore, we have:
\[ 5000 \left(1 + \frac{R}{100}\right)^2 - 5000 = 100R + 112.5 \]
- This equation can be solved for R.

**Conclusion for Statement I:**
Statement I is sufficient to find the value of R.

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**Step 2: Analyze Statement II**

Statement II states:
"Anurag invested Rs.X at R% p.a. at SI for 2 years and Rs.4000 at (R+5)% p.a. at SI for 3 years. Total interest received by him is Rs.4200."

1. **Calculate Simple Interest for Anurag's investments:**
- For the first investment:
\[ SI_1 = \frac{X \times R \times 2}{100} = \frac{2XR}{100} \]
- For the second investment:
\[ SI_2 = \frac{4000 \times (R + 5) \times 3}{100} = \frac{12000(R + 5)}{100} = 120R + 600 \]

2. **Set up the equation based on the information given:**
- The total interest received is:
\[ SI_1 + SI_2 = 4200 \]
- Therefore, we have:
\[ \frac{2XR}{100} + (120R + 600) = 4200 \]
- Rearranging gives:
\[ 2XR + 12000R + 60000 = 420000 \]
- This equation has two variables (X and R), making it impossible to solve for R alone.

**Conclusion for Statement II:**
Statement II is not sufficient to find the value of R.

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### Final Conclusion:
- Statement I is sufficient to answer the question.
- Statement II is not sufficient to answer the question.

Thus, the answer is that **Statement I alone is sufficient** to answer the question.