If A = `[3/7 "of" "4"1/5 div 18/25 + 17/24]` of `[289/16 div (3/4 + 2/3)^2 "of"8"]`,then the value of A as :

Options

A. A) 231
B. B) 213
C. C) 321
D. D) 132

Answer

To solve the problem step by step, we will break down the expression for A and calculate it systematically.

### Step 1: Simplify the expression for A
Given:
\[ A = \left[ \frac{3}{7} \text{ of } 4 \frac{1}{5} \div \frac{18}{25} + \frac{17}{24} \text{ of } \left( \frac{289}{16} \div \left( \frac{3}{4} + \frac{2}{3} \right)^2 \text{ of } 8 \right) \right] \]

### Step 2: Convert mixed number to improper fraction
Convert \( 4 \frac{1}{5} \) to an improper fraction:
\[ 4 \frac{1}{5} = \frac{21}{5} \]

### Step 3: Calculate \( \frac{3}{7} \text{ of } \frac{21}{5} \)
\[ \frac{3}{7} \text{ of } \frac{21}{5} = \frac{3}{7} \times \frac{21}{5} = \frac{63}{35} = \frac{9}{5} \]

### Step 4: Divide by \( \frac{18}{25} \)
Now, we need to divide \( \frac{9}{5} \) by \( \frac{18}{25} \):
\[ \frac{9}{5} \div \frac{18}{25} = \frac{9}{5} \times \frac{25}{18} = \frac{225}{90} = \frac{25}{10} = \frac{5}{2} \]

### Step 5: Calculate \( \frac{3}{4} + \frac{2}{3} \)
To find \( \frac{3}{4} + \frac{2}{3} \), we need a common denominator:
The LCM of 4 and 3 is 12.
\[ \frac{3}{4} = \frac{9}{12}, \quad \frac{2}{3} = \frac{8}{12} \]
So,
\[ \frac{3}{4} + \frac{2}{3} = \frac{9}{12} + \frac{8}{12} = \frac{17}{12} \]

### Step 6: Square the result
Now square \( \frac{17}{12} \):
\[ \left( \frac{17}{12} \right)^2 = \frac{289}{144} \]

### Step 7: Divide \( \frac{289}{16} \) by \( \frac{289}{144} \)
Now we divide:
\[ \frac{289}{16} \div \frac{289}{144} = \frac{289}{16} \times \frac{144}{289} = \frac{144}{16} = 9 \]

### Step 8: Calculate \( \frac{17}{24} \text{ of } 9 \)
Now we need to calculate:
\[ \frac{17}{24} \text{ of } 9 = \frac{17}{24} \times 9 = \frac{153}{24} = \frac{51}{8} \]

### Step 9: Add the two parts together
Now we add the two results:
\[ A = \frac{5}{2} + \frac{51}{8} \]
To add these, we need a common denominator:
The LCM of 2 and 8 is 8.
\[ \frac{5}{2} = \frac{20}{8} \]
So,
\[ A = \frac{20}{8} + \frac{51}{8} = \frac{71}{8} \]

### Final Result
Thus, the value of \( A \) is:
\[ A = \frac{71}{8} \]

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