The price of an article was first increased by 10% and then again by 20%. If the last increased price be 33, the original price was

Options

A. 30
B. 27.5
C. 26.5
D. 25

Answer

To find the original price of the article after two successive increases of 10% and 20%, we can follow these steps:

### Step 1: Understand the problem
We know that the final price after two increases is 33. The first increase is 10%, followed by a second increase of 20%.

### Step 2: Set up the equations
Let the original price be \( P \).

1. After a 10% increase, the price becomes:
\[ P + 0.10P = 1.10P \]

2. After a further 20% increase on the new price, the price becomes:
\[ 1.10P + 0.20(1.10P) = 1.10P \times 1.20 = 1.32P \]

### Step 3: Set the final price equal to 33
We know that the final price after both increases is 33:
\[ 1.32P = 33 \]

### Step 4: Solve for the original price \( P \)
To find \( P \), we divide both sides by 1.32:
\[ P = \frac{33}{1.32} \]

### Step 5: Calculate \( P \)
Now, we perform the division:
\[ P = \frac{33}{1.32} = 25 \]

### Conclusion
The original price of the article was \( 25 \).

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