`5/4` th of a number is 60 more than half of the same number the required number is :

Options

A. 50
B. 180
C. 90
D. 80

Answer

To solve the problem step by step, we can follow these instructions:

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

### Step 2: Set up the equation based on the problem statement
According to the problem, \( \frac{5}{4} \) of the number is 60 more than half of the same number. This can be expressed mathematically as:
\[ \frac{5}{4}x = \frac{1}{2}x + 60 \]

### Step 3: Simplify the equation
To simplify the equation, we first need to eliminate the fractions. The least common multiple (LCM) of the denominators (4 and 2) is 4. We can multiply the entire equation by 4 to eliminate the fractions:
\[ 4 \cdot \frac{5}{4}x = 4 \cdot \left(\frac{1}{2}x + 60\right) \]
This simplifies to:
\[ 5x = 2x + 240 \]

### Step 4: Rearrange the equation
Now, we will rearrange the equation to isolate \( x \):
\[ 5x - 2x = 240 \]
This simplifies to:
\[ 3x = 240 \]

### Step 5: Solve for \( x \)
Now, we can solve for \( x \) by dividing both sides by 3:
\[ x = \frac{240}{3} \]
Calculating this gives:
\[ x = 80 \]

### Conclusion
The required number is \( 80 \).

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