What well Centre in place of the question mark (?) in the following questions?
` 2 (1)/(3) " of " 1 (1)/(4) " of " (?) = 280`

Options

A. 84
B. 124
C. 96
D. 108

Answer

To solve the equation \( 2 \frac{1}{3} \text{ of } 1 \frac{1}{4} \text{ of } (?) = 280 \), we will first convert the mixed numbers into improper fractions.

### Step 1: Convert mixed numbers to improper fractions
- \( 2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{6 + 1}{3} = \frac{7}{3} \)
- \( 1 \frac{1}{4} = \frac{1 \times 4 + 1}{4} = \frac{4 + 1}{4} = \frac{5}{4} \)

Now, we can rewrite the equation:
\[ \frac{7}{3} \text{ of } \frac{5}{4} \text{ of } (?) = 280 \]

### Step 2: Rewrite the equation using multiplication
The phrase "of" can be replaced with multiplication:
\[ \frac{7}{3} \times \frac{5}{4} \times (?) = 280 \]

### Step 3: Calculate the product of the fractions
Now, let's calculate \( \frac{7}{3} \times \frac{5}{4} \):
\[ \frac{7 \times 5}{3 \times 4} = \frac{35}{12} \]

### Step 4: Substitute back into the equation
Now we substitute this back into the equation:
\[ \frac{35}{12} \times (?) = 280 \]

### Step 5: Isolate the variable (?)
To isolate \( (?) \), we can multiply both sides by the reciprocal of \( \frac{35}{12} \):
\[ (?) = 280 \times \frac{12}{35} \]

### Step 6: Simplify the right side
Now, we simplify \( 280 \times \frac{12}{35} \):
1. First, simplify \( \frac{280}{35} = 8 \) (since \( 280 \div 35 = 8 \)).
2. Now, multiply by 12:
\[ (?) = 8 \times 12 = 96 \]

### Final Answer
Thus, the value that should replace the question mark (?) is \( 96 \).

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