Whal will come in place of questron mark(?) in the following questions?
`(14)/(25)" of "6/(15)" of "5/7" of " 1350=?`

Options

A. 204
B. 216
C. 210
D. 212

Answer

To solve the problem step by step, we need to evaluate the expression:

\[ \frac{14}{25} \text{ of } \frac{6}{15} \text{ of } \frac{5}{7} \text{ of } 1350 \]

This can be rewritten using multiplication:

\[ \frac{14}{25} \times \frac{6}{15} \times \frac{5}{7} \times 1350 \]

### Step 1: Simplify the fractions

First, we can simplify the fractions before multiplying.

1. **Simplify \(\frac{6}{15}\)**:
\[ \frac{6}{15} = \frac{2}{5} \]

2. **Now, rewrite the expression**:
\[ \frac{14}{25} \times \frac{2}{5} \times \frac{5}{7} \times 1350 \]

### Step 2: Combine the fractions

Now we can multiply the fractions together:

\[ \frac{14 \times 2 \times 5}{25 \times 5 \times 7} \times 1350 \]

### Step 3: Cancel common factors

Let's cancel out the common factors. Notice that \(5\) in the numerator and denominator can be canceled:

\[ \frac{14 \times 2}{25 \times 7} \times 1350 \]

### Step 4: Calculate the denominator

Now calculate \(25 \times 7\):

\[ 25 \times 7 = 175 \]

### Step 5: Rewrite the expression

Now we can rewrite the expression:

\[ \frac{14 \times 2}{175} \times 1350 \]

### Step 6: Calculate \(14 \times 2\)

Calculate \(14 \times 2\):

\[ 14 \times 2 = 28 \]

### Step 7: Substitute back into the expression

Now substitute back into the expression:

\[ \frac{28}{175} \times 1350 \]

### Step 8: Simplify \(\frac{28}{175}\)

Now simplify \(\frac{28}{175}\):

\[ \frac{28}{175} = \frac{4}{25} \quad (\text{dividing both by } 7) \]

### Step 9: Multiply by 1350

Now we multiply:

\[ \frac{4}{25} \times 1350 \]

### Step 10: Calculate \(1350 \div 25\)

First, calculate \(1350 \div 25\):

\[ 1350 \div 25 = 54 \]

### Step 11: Multiply by 4

Now multiply by 4:

\[ 4 \times 54 = 216 \]

### Final Answer

Thus, the value that comes in place of the question mark is:

\[ \boxed{216} \]