Direction (41–52): What will come in the place of (?) mark in following question?

$\frac{5}{8}\text{of}\frac{4}{9}\text{of}\frac{3}{5}\text{of}\mathrm{ 654}=?$

The correct answer is 109.

To find the value that should replace the question mark (?), we need to simplify the given mathematical expression step-by-step. The word "of" in mathematical operations represents multiplication.

The given expression is:

$\frac{5}{8}\times \frac{4}{9}\times \frac{3}{5}\times 654=?$

Step 1: Simplify the product of the fractions first.
We can multiply the numerators together and the denominators together:

$\frac{5\times 4\times 3}{8\times 9\times 5}$

Step 2: Cancel out common terms in the numerator and denominator.
- The number 5 in the numerator cancels out the 5 in the denominator.
- This leaves us with:

$\frac{4\times 3}{8\times 9}$

Step 3: Further simplify the remaining numbers.
- We can simplify 4 in the numerator and 8 in the denominator (since 8 = 4 × 2):

$\frac{3}{2\times 9}$

- We can simplify 3 in the numerator and 9 in the denominator (since 9 = 3 × 3):

$\frac{1}{2\times 3}=\frac{1}{6}$

Step 4: Multiply the simplified fraction by 654.
Now we calculate the final value:

$\frac{1}{6}\times 654=\frac{654}{6}$

Performing the division:

$654÷6=109$

Therefore, the value that comes in place of the question mark is 109.