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Let's go through each question step by step.

### Given Data
- **Total loan amount:** Rs 72,000.
- **Ratios of loans:** 2:3:5:8 for persons A, B, C, and D respectively.
- **Interest Details:**
  - **Person A** - 20% per year for 1 year (Compound Interest, compounded half-yearly).
  - **Person B** - 15% per year for 3 years (Simple Interest).
  - **Person C** - 36% per year for 8 years (Simple Interest).
  - **Person D** - 25% per year for 6 years (Simple Interest).

#### Step 1: Calculating Loan Amounts Based on Ratios
The total loan amount of Rs 72,000 is divided in the ratio 2:3:5:8.

- **Sum of Ratios:** \(2 + 3 + 5 + 8 = 18\)
- **Loan for A:** \( \frac{2}{18} \times 72,000 = 8,000\)
- **Loan for B:** \( \frac{3}{18} \times 72,000 = 12,000\)
- **Loan for C:** \( \frac{5}{18} \times 72,000 = 20,000\)
- **Loan for D:** \( \frac{8}{18} \times 72,000 = 32,000\)

Now, let's address each question.

---

### Q113: Compound Interest on Person A's Loan
Person A borrowed Rs 8,000 at a 20% annual interest rate compounded half-yearly for 1 year.

For compound interest compounded half-yearly:
- **Rate per half-year:** \( \frac{20}{2} = 10\%\)
- **Number of periods:** \(2\) (since it's compounded twice in 1 year)

The compound interest formula is:
\[
A = P \left(1 + \frac{r}{100}\right)^n
\]
where:
- \(P = 8,000\),
- \(r = 10\%\), and
- \(n = 2\).

\[
A = 8000 \left(1 + \frac{10}{100}\right)^2 = 8000 \times 1.1^2 = 8000 \times 1.21 = 9680
\]
The compound interest is:
\[
9680 - 8000 = 1680
\]
**Answer to Q113:** (a) Rs. 1680.

---

### Q114: Who Will Return Less Simple Interest?
Simple interest formula: 
\[
SI = \frac{P \times R \times T}{100}
\]

1. **For Person B:** \( P = 12,000\), \( R = 15\%\), \( T = 3 \) years.
   \[
   SI_B = \frac{12000 \times 15 \times 3}{100} = 5400
   \]

2. **For Person C:** \( P = 20,000\), \( R = 36\%\), \( T = 8 \) years.
   \[
   SI_C = \frac{20000 \times 36 \times 8}{100} = 57600
   \]

3. **For Person D:** \( P = 32,000\), \( R = 25\%\), \( T = 6 \) years.
   \[
   SI_D = \frac{32000 \times 25 \times 6}{100} = 48000
   \]

Comparing these, **Person B returns the least interest**.

**Answer to Q114:** (b) B.

---

### Q115: Difference in Simple Interest Between C and D
We already calculated:
- \(SI_C = 57600\)
- \(SI_D = 48000\)

Difference:
\[
57600 - 48000 = 9600
\]

**Answer to Q115:** (a) Rs. 9600.

---

### Q116: Ratio of Simple Interest from A to B
1. **Person A's Simple Interest (for comparison purposes):**
   - Although A's interest is compound, if we consider it with simple interest, \( P = 8000\), \( R = 20\%\), \( T = 1 \) year.
   \[
   SI_A = \frac{8000 \times 20 \times 1}{100} = 1600
   \]

2. **Person B's Simple Interest:** Already calculated as \(5400\).

Ratio of \(SI_A : SI_B = 1600 : 5400\).

Simplifying,
\[
\frac{1600}{5400} = \frac{8}{27}
\]

**Answer to Q116:** (a) 8:27.

---

Would you like further explanation on any of these answers, or do you have additional questions?

### Related Questions
1. What is the difference between simple and compound interest, and why do they yield different results?
2. If Person A's loan was compounded quarterly instead of half-yearly, how would it affect the final amount?
3. How does the time period affect the amount of simple interest earned?
4. If Person D's interest rate was reduced to 20%, what would the new simple interest amount be?
5. What is the impact of the loan ratio on the total interest paid by each person?

### Tip
When solving compound interest problems, pay close attention to the compounding frequency (e.g., annually, semi-annually) as it affects the overall interest accrued.

Four persons borrowed money from the bank at different rates, either simple or compound interest, for different periods. The amounts lent to A, B, C, and D are in the ratio 2:3:5:8, and the total amount lent by all the persons is Rs 72,000. Answer questions about compound interest and simple interest for each person.

Explore a set of questions based on simple and compound interest calculations, including compound interest compounded half-yearly and simple interest differences based on different time periods. This set includes ratios, interest rates, and loan distribution.

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