The value of `120 -: [2/3 xx (1- 2/5) xx5] + [9/8 " of " 4/3 -: 3/4 " of " 2/3] +5/3` is :

Options

A. 62
B. 65
C. 63
D. 60

Answer

To solve the expression \( 120 -: \left[\frac{2}{3} \times \left(1 - \frac{2}{5}\right) \times 5\right] + \left[\frac{9}{8} \text{ of } \frac{4}{3} -: \frac{3}{4} \text{ of } \frac{2}{3}\right] + \frac{5}{3} \), we will follow the order of operations (BODMAS/BIDMAS).

### Step 1: Simplify the first bracket
First, we need to calculate \( 1 - \frac{2}{5} \):
\[ 1 - \frac{2}{5} = \frac{5}{5} - \frac{2}{5} = \frac{3}{5} \]

Now substitute this back into the first bracket:
\[ \frac{2}{3} \times \left(\frac{3}{5}\right) \times 5 \]

### Step 2: Calculate the first bracket
Now we can simplify:
\[ \frac{2}{3} \times \frac{3}{5} \times 5 = \frac{2}{3} \times 3 = 2 \]

### Step 3: Substitute back into the main expression
Now substitute this value back into the main expression:
\[ 120 -: 2 + \left[\frac{9}{8} \text{ of } \frac{4}{3} -: \frac{3}{4} \text{ of } \frac{2}{3}\right] + \frac{5}{3} \]

### Step 4: Calculate the second bracket
First, calculate \( \frac{9}{8} \text{ of } \frac{4}{3} \):
\[ \frac{9}{8} \times \frac{4}{3} = \frac{36}{24} = \frac{3}{2} \]

Next, calculate \( \frac{3}{4} \text{ of } \frac{2}{3} \):
\[ \frac{3}{4} \times \frac{2}{3} = \frac{6}{12} = \frac{1}{2} \]

Now substitute these values back into the second bracket:
\[ \frac{3}{2} -: \frac{1}{2} = \frac{3}{2} \div \frac{1}{2} = \frac{3}{2} \times 2 = 3 \]

### Step 5: Substitute back into the main expression
Now substitute this value back into the main expression:
\[ 120 -: 2 + 3 + \frac{5}{3} \]

### Step 6: Calculate \( 120 -: 2 \)
\[ 120 \div 2 = 60 \]

### Step 7: Combine all parts
Now we have:
\[ 60 + 3 + \frac{5}{3} \]

Convert \( 3 \) to a fraction with a denominator of \( 3 \):
\[ 3 = \frac{9}{3} \]

Now combine:
\[ 60 + \frac{9}{3} + \frac{5}{3} = 60 + \frac{14}{3} \]

### Step 8: Convert \( 60 \) to a fraction
Convert \( 60 \) to a fraction with a denominator of \( 3 \):
\[ 60 = \frac{180}{3} \]

Now combine:
\[ \frac{180}{3} + \frac{14}{3} = \frac{194}{3} \]

### Final Answer
Thus, the final value of the expression is:
\[ \frac{194}{3} \]