The average of `40%` of a number and `33%` of the same number is 73. The average of ` (1)/(5)` th and `(1)/(4)` th of that number is

Options

A. 40
B. 45
C. 42
D. 50

Answer

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

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

### Step 2: Calculate 40% and 33% of the number
- 40% of \( x \) is \( 0.4x \).
- 33% of \( x \) is \( 0.33x \).

### Step 3: Find the average of 40% and 33% of the number
The average of \( 0.4x \) and \( 0.33x \) is given by:
\[ \text{Average} = \frac{0.4x + 0.33x}{2} \]
This simplifies to:
\[ \text{Average} = \frac{(0.4 + 0.33)x}{2} = \frac{0.73x}{2} \]

### Step 4: Set the average equal to 73
According to the problem, this average equals 73:
\[ \frac{0.73x}{2} = 73 \]

### Step 5: Solve for \( x \)
To eliminate the fraction, multiply both sides by 2:
\[ 0.73x = 146 \]
Now, divide both sides by 0.73:
\[ x = \frac{146}{0.73} \approx 200 \]

### Step 6: Calculate \( \frac{1}{5} \) and \( \frac{1}{4} \) of \( x \)
Now, we need to find \( \frac{1}{5} \) and \( \frac{1}{4} \) of \( x \):
- \( \frac{1}{5} \) of \( x \) is \( \frac{200}{5} = 40 \).
- \( \frac{1}{4} \) of \( x \) is \( \frac{200}{4} = 50 \).

### Step 7: Find the average of \( \frac{1}{5} \) and \( \frac{1}{4} \) of \( x \)
The average of \( 40 \) and \( 50 \) is:
\[ \text{Average} = \frac{40 + 50}{2} = \frac{90}{2} = 45 \]

### Final Answer
The average of \( \frac{1}{5} \) and \( \frac{1}{4} \) of that number is **45**.

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