If a number is reduced by 35%, then it becomes 416. By how much percent should the number be increased so that it become 876.8?

Options

A. 33
B. 37
C. 34.2
D. 38.4

Answer

To solve the problem step by step, let's break it down:

### Step 1: Define the original number
Let the original number be \( x \).

### Step 2: Set up the equation for the reduction
If the number is reduced by 35%, it means that 65% of the original number remains. Therefore, we can write the equation:
\[ x - 0.35x = 416 \]
This simplifies to:
\[ 0.65x = 416 \]

### Step 3: Solve for \( x \)
To find \( x \), divide both sides of the equation by 0.65:
\[ x = \frac{416}{0.65} \]
Calculating this gives:
\[ x = 640 \]

### Step 4: Determine the required increase to reach 876.8
Next, we need to find out how much we need to increase \( x \) (which is 640) to reach 876.8. We calculate the difference:
\[ \text{Increase} = 876.8 - 640 = 236.8 \]

### Step 5: Calculate the percentage increase
Now, we find the percentage increase based on the original number \( x \):
\[ \text{Percentage Increase} = \left(\frac{\text{Increase}}{x}\right) \times 100 = \left(\frac{236.8}{640}\right) \times 100 \]
Calculating this gives:
\[ \text{Percentage Increase} = 0.37 \times 100 = 37\% \]

### Final Answer
Thus, the number should be increased by **37%** to become 876.8.

---