The difference between successive discounts of 40% followed by 30% and 45% followed by 20% on the marked price of an article is ₹ 12. The marked price of the article is:
किसी वस्तु के अंकित मूल्य पर 40% उसके बाद 30% और 45% उसके बाद 20% की उत्तरोत्तर छूट में अंतर ₹ 12 है। उस वस्तु का अंकित मूल्य है

Options

A. ₹200
B. ₹400
C. ₹800
D. ₹600

Explanation

To solve the problem, let's denote the marked price of the article as \( x \).

### Step 1: Calculate the final price after the first set of discounts (40% followed by 30%)
1. The first discount is 40%, so the price after the first discount is:
\[ \text{Price after 40% discount} = x - 0.4x = 0.6x \]
2. The second discount is 30% on the new price (0.6x), so the price after the second discount is:
\[ \text{Price after 30% discount} = 0.6x - 0.3(0.6x) = 0.6x - 0.18x = 0.42x \]

### Step 2: Calculate the final price after the second set of discounts (45% followed by 20%)
1. The first discount is 45%, so the price after the first discount is:
\[ \text{Price after 45% discount} = x - 0.45x = 0.55x \]
2. The second discount is 20% on the new price (0.55x), so the price after the second discount is:
\[ \text{Price after 20% discount} = 0.55x - 0.2(0.55x) = 0.55x - 0.11x = 0.44x \]

### Step 3: Set up the equation based on the difference between the two final prices
The difference between the two final prices is given as ₹ 12:
\[ 0.42x - 0.44x = -0.02x \]
Since the difference is given as ₹ 12, we can write:
\[ 0.02x = 12 \]

### Step 4: Solve for \( x \)
To find \( x \), divide both sides by 0.02:
\[ x = \frac{12}{0.02} = 600 \]

### Conclusion
The marked price of the article is ₹ 600.

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