If the cost of an article is Rs. P after two successive reductions of 20% and 25%, the original price of the article was

Options

A. Rs. `(5P)/(3)`
B. Rs. `(4P)/(5)`
C. Rs. `(3P)/(5)`
D. Rs. `(5P)/(4)`

Answer

To find the original price of an article after two successive reductions of 20% and 25%, we can follow these steps:

### Step 1: Understand the successive discounts
The article undergoes two successive discounts: first 20%, then 25%. This means that the price is reduced by 20% of the original price, and then the new price is reduced by 25%.

### Step 2: Calculate the price after the first discount
Let the original price be \( x \).
After a 20% discount, the price becomes:
\[ \text{Price after 20% discount} = x - 0.20x = 0.80x \]

### Step 3: Calculate the price after the second discount
Now, we apply a 25% discount on the new price \( 0.80x \):
\[ \text{Price after 25% discount} = 0.80x - 0.25(0.80x) = 0.80x - 0.20x = 0.60x \]

### Step 4: Set the final price equal to \( P \)
According to the problem, the final price after both discounts is given as \( P \):
\[ 0.60x = P \]

### Step 5: Solve for the original price \( x \)
To find \( x \), we rearrange the equation:
\[ x = \frac{P}{0.60} = \frac{P}{\frac{3}{5}} = P \times \frac{5}{3} \]

### Final Answer
Thus, the original price of the article was:
\[ \text{Original Price} = \frac{5P}{3} \]

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