If 24 is deducted from 45% of a number result becomes 48. What will be 3/8 part of that number?

Options

A. a. 140
B. b. 130
C. c. 145
D. d. 60

Answer

Let's solve the problem step by step.

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

### Step 2: Set up the equation
According to the problem, if 24 is deducted from 45% of the number, the result is 48. This can be expressed mathematically as:
\[ 0.45x - 24 = 48 \]

### Step 3: Isolate the term with \( x \)
To isolate \( 0.45x \), we add 24 to both sides of the equation:
\[ 0.45x = 48 + 24 \]
\[ 0.45x = 72 \]

### Step 4: Solve for \( x \)
Next, we need to solve for \( x \) by dividing both sides by 0.45:
\[ x = \frac{72}{0.45} \]

### Step 5: Simplify the division
To simplify \( \frac{72}{0.45} \), we can multiply the numerator and denominator by 100 to eliminate the decimal:
\[ x = \frac{72 \times 100}{45} = \frac{7200}{45} \]

### Step 6: Perform the division
Now, we divide 7200 by 45:
\[ x = 160 \]

### Step 7: Find \( \frac{3}{8} \) of the number
Now that we have found \( x = 160 \), we need to calculate \( \frac{3}{8} \) of this number:
\[ \frac{3}{8} \times 160 \]

### Step 8: Simplify the multiplication
To find \( \frac{3}{8} \times 160 \), we can simplify:
\[ \frac{160}{8} = 20 \]
Then multiply by 3:
\[ 3 \times 20 = 60 \]

### Final Answer
Thus, \( \frac{3}{8} \) part of the number is \( 60 \).

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