Simplify:- 6/5 of 3/4 of 1/2 of ? = 3600

Options

A. a. 6000
B. b. 7000
C. c. 8000
D. d. 18000

Answer

To solve the equation \( \frac{6}{5} \times \frac{3}{4} \times \frac{1}{2} \times ? = 3600 \), we will follow these steps:

### Step 1: Set up the equation
We start with the equation:
\[ \frac{6}{5} \times \frac{3}{4} \times \frac{1}{2} \times x = 3600 \]
where \( x \) is the unknown quantity we need to find.

### Step 2: Calculate the product of the fractions
First, we need to multiply the fractions on the left side:
\[ \frac{6}{5} \times \frac{3}{4} \times \frac{1}{2} \]
Calculating this step by step:
- Multiply the numerators: \( 6 \times 3 \times 1 = 18 \)
- Multiply the denominators: \( 5 \times 4 \times 2 = 40 \)

So, we have:
\[ \frac{18}{40} \]

### Step 3: Simplify the fraction
Next, we simplify \( \frac{18}{40} \):
- The greatest common divisor (GCD) of 18 and 40 is 2.
- Dividing both the numerator and the denominator by 2 gives:
\[ \frac{18 \div 2}{40 \div 2} = \frac{9}{20} \]

### Step 4: Substitute back into the equation
Now we substitute back into our equation:
\[ \frac{9}{20} \times x = 3600 \]

### Step 5: Isolate \( x \)
To isolate \( x \), we multiply both sides by the reciprocal of \( \frac{9}{20} \):
\[ x = 3600 \times \frac{20}{9} \]

### Step 6: Calculate \( x \)
Now we calculate \( x \):
\[ x = 3600 \times \frac{20}{9} = \frac{72000}{9} \]
Now, divide 72000 by 9:
\[ 72000 \div 9 = 8000 \]

### Final Answer
Thus, the value of \( ? \) is:
\[ x = 8000 \]

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