Question

If a given number is increased by 25% , the number becomes 320. The given number is

• A. 286
• B. 264
• C. 276
• D. 256

Hint:

An increase of 25% is equivalent to multiplying the original number by $\frac{5}{4}$.
To find the original number, simply multiply the final number by its reciprocal: $320 \times \frac{4}{5} = 64 \times 4 = 256$.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
We are given that when a certain number is increased by 25%, the resulting value is 320.
We need to find the original value of this number.

Step 2: Key Formula or Approach:
Let the original number be represented by the variable $x$.
An increase of 25% on $x$ can be mathematically represented as:
\[ x + 25\% \text{ of } x = 320 \]
This can be simplified using decimal or fractional representations:
\[ x + 0.25x = 320 \implies 1.25x = 320 \]
Or using fractions:
\[ x \left(1 + \frac{25}{100}\right) = 320 \implies x \left(\frac{125}{100}\right) = 320 \implies x \left(\frac{5}{4}\right) = 320 \]

Step 3: Detailed Calculation:
Using the fractional equation, we solve for $x$ step-by-step:
\[ \frac{5}{4}x = 320 \]
Multiply both sides of the equation by 4:
\[ 5x = 320 \times 4 \]
\[ 5x = 1280 \]
Now, divide both sides by 5:
\[ x = \frac{1280}{5} \]
\[ x = 256 \]
Let's verify the result:
- Original number: 256
- 25% of 256:
\[ \frac{25}{100} \times 256 = \frac{1}{4} \times 256 = 64 \]
- Increased value:
\[ 256 + 64 = 320 \]
The calculation is verified.

Step 4: Final Answer:
The original number is 256, which corresponds to Option (D).