What will come in place of the question mark (?) in the given questions ?
`(1 7/60)/(1 27/40)xx(1 29/34)xx?=231`

Options

A. 153
B. 182
C. 221
D. 187

Answer

To solve the equation `(1 7/60)/(1 27/40)xx(1 29/34)xx?=231`, we will follow these steps:

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

1. **Convert \(1 \frac{7}{60}\)**:
\[ 1 \frac{7}{60} = \frac{60 \times 1 + 7}{60} = \frac{67}{60} \]

2. **Convert \(1 \frac{27}{40}\)**:
\[ 1 \frac{27}{40} = \frac{40 \times 1 + 27}{40} = \frac{67}{40} \]

3. **Convert \(1 \frac{29}{34}\)**:
\[ 1 \frac{29}{34} = \frac{34 \times 1 + 29}{34} = \frac{63}{34} \]

### Step 2: Rewrite the Equation
Now we can rewrite the original equation using the improper fractions we just calculated:
\[ \frac{67}{60} \div \frac{67}{40} \times \frac{63}{34} \times ? = 231 \]

### Step 3: Simplify the Division
To simplify the division, we can multiply by the reciprocal:
\[ \frac{67}{60} \times \frac{40}{67} \times \frac{63}{34} \times ? = 231 \]

The \(67\) in the numerator and denominator cancels out:
\[ \frac{40}{60} \times \frac{63}{34} \times ? = 231 \]

### Step 4: Simplify Further
Now simplify \(\frac{40}{60}\):
\[ \frac{40}{60} = \frac{2}{3} \]
Thus, the equation becomes:
\[ \frac{2}{3} \times \frac{63}{34} \times ? = 231 \]

### Step 5: Multiply the Fractions
Now multiply \(\frac{2}{3} \times \frac{63}{34}\):
\[ \frac{2 \times 63}{3 \times 34} = \frac{126}{102} \]
This can be simplified:
\[ \frac{126}{102} = \frac{21}{17} \quad (\text{dividing both numerator and denominator by 6}) \]

### Step 6: Set Up the Equation
Now our equation looks like:
\[ \frac{21}{17} \times ? = 231 \]

### Step 7: Solve for ?
To find \(?\), we can multiply both sides by the reciprocal of \(\frac{21}{17}\):
\[ ? = 231 \times \frac{17}{21} \]

### Step 8: Calculate the Value
Now calculate \(231 \times \frac{17}{21}\):
\[ ? = 231 \times \frac{17}{21} = 231 \div 21 \times 17 = 11 \times 17 = 187 \]

### Final Answer
Thus, the value that comes in place of the question mark (?) is **187**.