Quantity I : Ratio of CP to MP of an article is 19 : 30 Shopkeeper allowed `24%` discount and earned `20%` profit on selling the article. If SP of the article is Rs. 912 then find difference between amount of profit earned and amount of discount allowed (in Rs.)
Quantity II. Shopkeeper marked an article `70%` above its cost price andhe allowed ` 40%` discount on it . If shopkeeper sold the article at Rs. 183.6 then find sum of amount of profit earned and amount of discount allowed (in Rs. )

Options

A. Quantity I ` lt ` Quantity II
B. Quantity I ` le ` Quantity II
C. Quantity I ` gt ` Quantity II
D. Quantity I ` ge ` Quantity II

Answer

To solve the problem, we will break it down into two parts: Quantity I and Quantity II.

### Quantity I

1. **Understanding the Ratios**:
- The ratio of Cost Price (CP) to Market Price (MP) is given as 19:30.
- Let CP = 19x and MP = 30x for some value of x.

2. **Finding the Selling Price (SP)**:
- The Selling Price (SP) is given as Rs. 912.

3. **Calculating the Discount**:
- The shopkeeper allowed a discount of 24% on the Market Price (MP).
- Discount = 24% of MP = 0.24 * MP = 0.24 * 30x = 7.2x.
- Therefore, SP = MP - Discount = 30x - 7.2x = 22.8x.
- Setting this equal to the given SP:
\[ 22.8x = 912 \]
- Solving for x:
\[ x = \frac{912}{22.8} = 40 \]

4. **Calculating CP and MP**:
- Now, substituting x back to find CP and MP:
\[ CP = 19x = 19 * 40 = 760 \]
\[ MP = 30x = 30 * 40 = 1200 \]

5. **Calculating Profit**:
- The profit earned is given as 20% of CP.
- Profit = 20% of CP = 0.20 * 760 = 152.

6. **Calculating the Amount of Discount**:
- We already calculated the discount as 7.2x:
\[ Discount = 7.2 * 40 = 288. \]

7. **Finding the Difference**:
- Now, we need to find the difference between the profit earned and the discount allowed:
\[ Difference = Profit - Discount = 152 - 288 = -136. \]

### Quantity II

1. **Understanding the Marked Price**:
- The shopkeeper marked an article 70% above its cost price.
- Let CP = y, then MP = CP + 70% of CP = y + 0.70y = 1.70y.

2. **Calculating the Selling Price (SP)**:
- The shopkeeper allowed a discount of 40% on the marked price.
- Discount = 40% of MP = 0.40 * 1.70y = 0.68y.
- Therefore, SP = MP - Discount = 1.70y - 0.68y = 1.02y.

3. **Setting the Selling Price**:
- The SP is given as Rs. 183.6.
- Setting this equal to the calculated SP:
\[ 1.02y = 183.6 \]
- Solving for y:
\[ y = \frac{183.6}{1.02} = 180. \]

4. **Calculating CP and MP**:
- Now substituting back to find CP and MP:
\[ CP = y = 180, \]
\[ MP = 1.70y = 1.70 * 180 = 306. \]

5. **Calculating Profit**:
- Profit = SP - CP = 183.6 - 180 = 3.6.

6. **Calculating the Amount of Discount**:
- We already calculated the discount:
\[ Discount = 0.68y = 0.68 * 180 = 122.4. \]

7. **Finding the Sum**:
- Finally, we need to find the sum of the profit earned and the discount allowed:
\[ Sum = Profit + Discount = 3.6 + 122.4 = 126. \]

### Final Answer
- **Quantity I**: Difference = -136.
- **Quantity II**: Sum = 126.