What will come in the place of question mark (?) in the following questions ?
`5/6" of "2""1/3" of "90%" of "420=?`

Options

A. 735
B. 756
C. 635
D. 376

Answer

To solve the equation \( \frac{5}{6} \) of \( 2 \frac{1}{3} \) of \( 90\% \) of \( 420 \), we will break it down step by step.

### Step 1: Convert Mixed Number to Improper Fraction
First, we need to convert \( 2 \frac{1}{3} \) into an improper fraction.
\[ 2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{6 + 1}{3} = \frac{7}{3} \]

### Step 2: Convert Percentage to Decimal
Next, we convert \( 90\% \) into a decimal.
\[ 90\% = \frac{90}{100} = 0.9 \]

### Step 3: Set Up the Equation
Now we can set up the equation using the values we have:
\[ \frac{5}{6} \times \frac{7}{3} \times 0.9 \times 420 \]

### Step 4: Calculate Step by Step
1. First, calculate \( 0.9 \times 420 \):
\[ 0.9 \times 420 = 378 \]

2. Now, substitute this back into the equation:
\[ \frac{5}{6} \times \frac{7}{3} \times 378 \]

3. Next, calculate \( \frac{5}{6} \times \frac{7}{3} \):
\[ \frac{5 \times 7}{6 \times 3} = \frac{35}{18} \]

4. Now multiply this by \( 378 \):
\[ \frac{35}{18} \times 378 \]

5. Simplify \( 378 \) by \( 18 \):
\[ 378 \div 18 = 21 \]

6. Now multiply \( 35 \) by \( 21 \):
\[ 35 \times 21 = 735 \]

### Final Answer
Thus, the final result is:
\[ 735 \]