`(6/7+(7 3/4-6 1/2)/(7/3xx9))` of ₹ 42 is equal to:

Options

A. ₹ 77
B. ₹ 38
C. ₹ 38.50
D. ₹ 39.50

Answer

To solve the expression \((6/7 + (7 \frac{3}{4} - 6 \frac{1}{2}) / (7/3 \times 9))\) of ₹ 42, we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
Convert \(7 \frac{3}{4}\) and \(6 \frac{1}{2}\) into improper fractions:
- \(7 \frac{3}{4} = \frac{7 \times 4 + 3}{4} = \frac{28 + 3}{4} = \frac{31}{4}\)
- \(6 \frac{1}{2} = \frac{6 \times 2 + 1}{2} = \frac{12 + 1}{2} = \frac{13}{2}\)

### Step 2: Substitute Back into the Expression
Now substitute these values back into the expression:
\[ (6/7 + (\frac{31}{4} - \frac{13}{2}) / (7/3 \times 9)) \]

### Step 3: Simplify the Fraction in the Parentheses
Next, we need to simplify \(\frac{31}{4} - \frac{13}{2}\):
- To subtract, we need a common denominator. The common denominator of 4 and 2 is 4.
- Convert \(\frac{13}{2}\) to have a denominator of 4:
\[ \frac{13}{2} = \frac{13 \times 2}{2 \times 2} = \frac{26}{4} \]
- Now perform the subtraction:
\[ \frac{31}{4} - \frac{26}{4} = \frac{31 - 26}{4} = \frac{5}{4} \]

### Step 4: Calculate the Denominator
Now calculate the denominator \(7/3 \times 9\):
\[ \frac{7}{3} \times 9 = \frac{7 \times 9}{3} = \frac{63}{3} = 21 \]

### Step 5: Substitute Back into the Expression
Now substitute back into the expression:
\[ (6/7 + \frac{5/4}{21}) \]

### Step 6: Simplify the Fraction
Now simplify \(\frac{5/4}{21}\):
\[ \frac{5/4}{21} = \frac{5}{4 \times 21} = \frac{5}{84} \]

### Step 7: Add the Fractions
Now add \(6/7\) and \(5/84\):
- Find a common denominator for \(7\) and \(84\), which is \(84\):
\[ 6/7 = \frac{6 \times 12}{7 \times 12} = \frac{72}{84} \]
- Now add:
\[ \frac{72}{84} + \frac{5}{84} = \frac{72 + 5}{84} = \frac{77}{84} \]

### Step 8: Multiply by ₹ 42
Now multiply \(\frac{77}{84}\) by ₹ 42:
\[ \frac{77}{84} \times 42 = \frac{77 \times 42}{84} \]
- Simplifying:
\[ \frac{77 \times 42}{84} = \frac{77 \times 1}{2} = \frac{77}{2} = 38.5 \]

### Final Answer
Thus, the final answer is ₹ 38.5.