What should come in place of the question mark(?) inthe following questions?
`2 (1)/(3)` of 1 `(1)/(4) of ( ? ) = 280`

Options

A. 116
B. 124
C. 48
D. 96

Answer

To solve the equation \( 2 \frac{1}{3} \) of \( 1 \frac{1}{4} \) of \( (?) = 280 \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers into improper fractions.

- For \( 2 \frac{1}{3} \):
\[ 2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{6 + 1}{3} = \frac{7}{3} \]

- For \( 1 \frac{1}{4} \):
\[ 1 \frac{1}{4} = \frac{1 \times 4 + 1}{4} = \frac{4 + 1}{4} = \frac{5}{4} \]

### Step 2: Set Up the Equation
Now we can rewrite the equation using the improper fractions:
\[ \frac{7}{3} \times \frac{5}{4} \times (?) = 280 \]

### Step 3: Multiply the Fractions
Next, we multiply the fractions on the left side:
\[ \frac{7 \times 5}{3 \times 4} \times (?) = 280 \]
This simplifies to:
\[ \frac{35}{12} \times (?) = 280 \]

### Step 4: Isolate the Question Mark
To isolate \( (?) \), we can multiply both sides by the reciprocal of \( \frac{35}{12} \):
\[ (?) = 280 \times \frac{12}{35} \]

### Step 5: Calculate the Right Side
Now we will calculate the right side:
\[ 280 \times \frac{12}{35} = \frac{280 \times 12}{35} \]

### Step 6: Simplify the Fraction
First, simplify \( \frac{280}{35} \):
\[ \frac{280}{35} = 8 \]
Now multiply by 12:
\[ 8 \times 12 = 96 \]

### Final Answer
Thus, the value that should come in place of the question mark is:
\[ ? = 96 \]

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