What will come in place of the question mark (?) in the given questions ?
`(2 2/5+3 1/4-2 7/8)xx?=222`

Options

A. 42
B. 80
C. 60
D. 62

Answer

To solve the equation \( (2 \frac{2}{5} + 3 \frac{1}{4} - 2 \frac{7}{8}) \times ? = 222 \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
1. Convert \( 2 \frac{2}{5} \):
\[ 2 \frac{2}{5} = \frac{5 \times 2 + 2}{5} = \frac{10 + 2}{5} = \frac{12}{5} \]

2. Convert \( 3 \frac{1}{4} \):
\[ 3 \frac{1}{4} = \frac{4 \times 3 + 1}{4} = \frac{12 + 1}{4} = \frac{13}{4} \]

3. Convert \( 2 \frac{7}{8} \):
\[ 2 \frac{7}{8} = \frac{8 \times 2 + 7}{8} = \frac{16 + 7}{8} = \frac{23}{8} \]

### Step 2: Substitute the Improper Fractions into the Equation
Now, substitute these values into the equation:
\[ \left( \frac{12}{5} + \frac{13}{4} - \frac{23}{8} \right) \times ? = 222 \]

### Step 3: Find a Common Denominator
The least common multiple (LCM) of the denominators \( 5, 4, \) and \( 8 \) is \( 40 \).

### Step 4: Convert Each Fraction
1. Convert \( \frac{12}{5} \) to a fraction with a denominator of \( 40 \):
\[ \frac{12}{5} = \frac{12 \times 8}{5 \times 8} = \frac{96}{40} \]

2. Convert \( \frac{13}{4} \) to a fraction with a denominator of \( 40 \):
\[ \frac{13}{4} = \frac{13 \times 10}{4 \times 10} = \frac{130}{40} \]

3. Convert \( \frac{23}{8} \) to a fraction with a denominator of \( 40 \):
\[ \frac{23}{8} = \frac{23 \times 5}{8 \times 5} = \frac{115}{40} \]

### Step 5: Combine the Fractions
Now, combine the fractions:
\[ \frac{96}{40} + \frac{130}{40} - \frac{115}{40} = \frac{96 + 130 - 115}{40} = \frac{111}{40} \]

### Step 6: Substitute Back into the Equation
Now substitute back into the equation:
\[ \left( \frac{111}{40} \right) \times ? = 222 \]

### Step 7: Solve for ?
To isolate \( ? \), multiply both sides by the reciprocal of \( \frac{111}{40} \):
\[ ? = 222 \times \frac{40}{111} \]

### Step 8: Calculate the Value
Now calculate:
\[ ? = \frac{222 \times 40}{111} = \frac{8880}{111} = 80 \]

### Final Answer
Thus, the value that comes in place of the question mark (?) is \( 80 \).

---