Read the statements carefully and select the correct option.
Statement-I : If a trader offers two successive discounts of 13% and 8% on an almirah marked for Rs 20000, then its selling price is Rs 16008.
Statement-II : On selling a laptop for Rs 84000, the shopkeeper lost 20%. To gain 10%, he should have sold it for Rs 115500.

Options

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

Answer

To solve the problem, we need to analyze both statements one by one.

### Statement I:
**If a trader offers two successive discounts of 13% and 8% on an almirah marked for Rs 20000, then its selling price is Rs 16008.**

1. **Calculate the total discount:**
- The formula for calculating the total discount when two successive discounts are applied is:
\[ \text{Total Discount} = x + y - \left(\frac{x \cdot y}{100}\right) \]
- Here, \(x = 13\%\) and \(y = 8\%\).
- Plugging in the values:
\[ \text{Total Discount} = 13 + 8 - \left(\frac{13 \cdot 8}{100}\right) \]
\[ = 21 - \left(\frac{104}{100}\right) \]
\[ = 21 - 1.04 = 19.96\% \]

2. **Calculate the selling price:**
- The selling price (SP) can be calculated using the formula:
\[ \text{SP} = \text{Marked Price} - \text{Discount} \]
- The marked price (MP) is Rs 20000.
- The discount amount is:
\[ \text{Discount Amount} = \frac{19.96}{100} \times 20000 = 3992 \]
- Therefore, the selling price is:
\[ \text{SP} = 20000 - 3992 = 16008 \]

**Conclusion for Statement I:** The selling price is indeed Rs 16008. Therefore, Statement I is **True**.

---

### Statement II:
**On selling a laptop for Rs 84000, the shopkeeper lost 20%. To gain 10%, he should have sold it for Rs 115500.**

1. **Calculate the cost price (CP) of the laptop:**
- If the selling price (SP) is Rs 84000 and there is a loss of 20%, then:
\[ \text{SP} = \text{CP} \times \left(1 - \frac{20}{100}\right) \]
- This means:
\[ 84000 = \text{CP} \times 0.8 \]
- Rearranging gives:
\[ \text{CP} = \frac{84000}{0.8} = 105000 \]

2. **Calculate the selling price for a gain of 10%:**
- To find the selling price for a gain of 10%, we use:
\[ \text{SP} = \text{CP} \times \left(1 + \frac{10}{100}\right) \]
- Plugging in the cost price:
\[ \text{SP} = 105000 \times 1.1 = 115500 \]

**Conclusion for Statement II:** The selling price to gain 10% is indeed Rs 115500. Therefore, Statement II is **True**.

---

### Final Conclusion:
Both statements are true. The correct option is that both Statement I and Statement II are correct.

---