If the difference between discount of 40% and two successive discounts of 20% on a certain article is Rs. 64, then what is the price (in Rs) of the article?

Options

A. 1500
B. 1280
C. 1440
D. 1600

Answer

To solve the problem, we need to find the price of an article given the difference between a single discount and two successive discounts. Here’s a step-by-step breakdown of the solution:

### Step 1: Define the Price of the Article
Let the price of the article be \( x \).

### Step 2: Calculate the Sale Price with a 40% Discount
The discount amount for a 40% discount is:
\[ \text{Discount} = 40\% \text{ of } x = \frac{40}{100} \times x = \frac{2}{5}x \]
Thus, the sale price after a 40% discount is:
\[ \text{Sale Price} = x - \frac{2}{5}x = \frac{3}{5}x \]

### Step 3: Calculate the Sale Price with Two Successive 20% Discounts
First, calculate the sale price after the first 20% discount:
\[ \text{First Discount} = 20\% \text{ of } x = \frac{20}{100} \times x = \frac{1}{5}x \]
So, the sale price after the first 20% discount is:
\[ \text{Sale Price after 1st Discount} = x - \frac{1}{5}x = \frac{4}{5}x \]

Now, apply the second 20% discount on the new sale price:
\[ \text{Second Discount} = 20\% \text{ of } \frac{4}{5}x = \frac{20}{100} \times \frac{4}{5}x = \frac{4}{25}x \]
Thus, the final sale price after both discounts is:
\[ \text{Final Sale Price} = \frac{4}{5}x - \frac{4}{25}x \]

### Step 4: Find a Common Denominator for the Final Sale Price
To subtract these fractions, we need a common denominator:
\[ \frac{4}{5}x = \frac{20}{25}x \]
So,
\[ \text{Final Sale Price} = \frac{20}{25}x - \frac{4}{25}x = \frac{16}{25}x \]

### Step 5: Set Up the Equation for the Difference in Discounts
According to the problem, the difference between the sale price with a 40% discount and the sale price with two successive 20% discounts is Rs. 64:
\[ \frac{3}{5}x - \frac{16}{25}x = 64 \]

### Step 6: Find a Common Denominator to Solve the Equation
The common denominator for \( \frac{3}{5}x \) and \( \frac{16}{25}x \) is 25:
\[ \frac{3}{5}x = \frac{15}{25}x \]
Now, substitute:
\[ \frac{15}{25}x - \frac{16}{25}x = 64 \]
This simplifies to:
\[ -\frac{1}{25}x = 64 \]

### Step 7: Solve for \( x \)
Multiply both sides by -25 to isolate \( x \):
\[ x = 64 \times -25 = -1600 \]
Since price cannot be negative, we take the absolute value:
\[ x = 1600 \]

### Conclusion
The price of the article is Rs. 1600.

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