A numbre is first increased by 20% and then reduced by 15% If the final value is 2040. then what is the intitial value of the number ?

Options

A. 2100
B. 1800
C. 2000
D. 1900

Answer

To solve the problem step by step, we will denote the initial number as \( X \).

### Step 1: Increase the number by 20%
When the number \( X \) is increased by 20%, the new value becomes:
\[ X + 0.20X = 1.20X \]

### Step 2: Reduce the new value by 15%
Now, we need to reduce this new value \( 1.20X \) by 15%. The reduction can be calculated as follows:
\[ 1.20X - 0.15(1.20X) = 1.20X \times (1 - 0.15) = 1.20X \times 0.85 = 1.02X \]

### Step 3: Set the final value equal to 2040
According to the problem, after these operations, the final value is given as 2040. Therefore, we can set up the equation:
\[ 1.02X = 2040 \]

### Step 4: Solve for \( X \)
To find the initial value \( X \), we will divide both sides of the equation by 1.02:
\[ X = \frac{2040}{1.02} \]

### Step 5: Calculate the value
Now, we will perform the division:
\[ X = 2000 \]

Thus, the initial value of the number is \( 2000 \).

### Final Answer
The initial value of the number is \( 2000 \).

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