What should come in place of the question mark (? ) in the following questions ?
`3/4 th of 3/5of 2/3` rd of ? = 3174

Options

A. 10550
B. 10540
C. 10580
D. 10500

Answer

To solve the equation \( \frac{3}{4} \text{ of } \frac{3}{5} \text{ of } \frac{2}{3} \text{ of } ? = 3174 \), we will follow these steps:

### Step 1: Write the equation in mathematical form
We can express the problem mathematically as:
\[ \frac{3}{4} \times \frac{3}{5} \times \frac{2}{3} \times ? = 3174 \]

### Step 2: Simplify the left side of the equation
First, we can multiply the fractions on the left side:
\[ \frac{3}{4} \times \frac{3}{5} \times \frac{2}{3} = \frac{3 \times 3 \times 2}{4 \times 5 \times 3} \]
The \(3\) in the numerator and denominator cancels out:
\[ = \frac{3 \times 2}{4 \times 5} = \frac{6}{20} \]
Now, simplify \(\frac{6}{20}\):
\[ = \frac{3}{10} \]

### Step 3: Substitute back into the equation
Now, substitute this back into the equation:
\[ \frac{3}{10} \times ? = 3174 \]

### Step 4: Solve for the question mark (?)
To isolate the question mark, multiply both sides by the reciprocal of \(\frac{3}{10}\):
\[ ? = 3174 \times \frac{10}{3} \]

### Step 5: Calculate the right side
Now, calculate \(3174 \times \frac{10}{3}\):
\[ ? = \frac{31740}{3} \]
Now, divide \(31740\) by \(3\):
\[ ? = 10580 \]

### Final Answer
Thus, the value that should come in place of the question mark is:
\[ ? = 10580 \]

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