What is the difference between a single discount of 50% and a single discount equivalent to two successive discounts of 42% and 8%, being given on shopping of rupees 3000?

Options

A. `100.8`
B. `96.4`
C. `104.6`
D. No difference

Answer

To solve the problem, we need to calculate the final price after applying a single discount of 50% and then compare it with the final price after applying two successive discounts of 42% and 8%. Finally, we will find the difference between these two amounts.

### Step 1: Calculate the final price after a single discount of 50%
1. **Original Price**: Rs. 3000
2. **Single Discount**: 50% of Rs. 3000
\[ \text{Discount Amount} = \frac{50}{100} \times 3000 = 1500 \]
3. **Final Price after 50% Discount**:
\[ \text{Final Price} = 3000 - 1500 = 1500 \]

### Step 2: Calculate the final price after successive discounts of 42% and 8%
1. **First Discount (42%)**:
- Calculate the amount after the first discount:
\[ \text{Discount Amount} = \frac{42}{100} \times 3000 = 1260 \]
- Price after first discount:
\[ \text{Price after 42% Discount} = 3000 - 1260 = 1740 \]

2. **Second Discount (8%)**:
- Calculate the amount after the second discount on the new price (Rs. 1740):
\[ \text{Discount Amount} = \frac{8}{100} \times 1740 = 139.2 \]
- Final Price after both discounts:
\[ \text{Final Price} = 1740 - 139.2 = 1600.8 \]

### Step 3: Calculate the difference between the two final prices
1. **Difference**:
\[ \text{Difference} = \text{Final Price with 50% Discount} - \text{Final Price with Successive Discounts} \]
\[ \text{Difference} = 1500 - 1600.8 = -100.8 \]

### Conclusion
The difference between a single discount of 50% and a single discount equivalent to two successive discounts of 42% and 8% on a shopping amount of Rs. 3000 is Rs. -100.8. This indicates that the single discount of 50% is actually better than the successive discounts.

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