What will come in place of question mark (?) in the following questions ?
`(2)/(5)` of `(13)/(4)` of `(5)/(26)` of ? = 32.5

Options

A. 694
B. 780
C. 684
D. None of these

Answer

To solve the equation \(\frac{2}{5}\) of \(\frac{13}{4}\) of \(\frac{5}{26}\) of \(?\) = 32.5, we can follow these steps:

### Step 1: Rewrite the equation using multiplication
The term "of" can be replaced by multiplication. Thus, we can rewrite the equation as:
\[ \frac{2}{5} \times \frac{13}{4} \times \frac{5}{26} \times ? = 32.5 \]

### Step 2: Simplify the left side
Now, we will simplify the left side of the equation step by step:
1. Multiply \(\frac{2}{5}\) and \(\frac{13}{4}\):
\[ \frac{2 \times 13}{5 \times 4} = \frac{26}{20} \]
This can be simplified to:
\[ \frac{13}{10} \]

2. Now multiply \(\frac{13}{10}\) by \(\frac{5}{26}\):
\[ \frac{13 \times 5}{10 \times 26} = \frac{65}{260} \]
This can be simplified to:
\[ \frac{1}{4} \]

### Step 3: Set up the equation
Now we have:
\[ \frac{1}{4} \times ? = 32.5 \]

### Step 4: Solve for \(?\)
To find \(?\), multiply both sides of the equation by 4:
\[ ? = 32.5 \times 4 \]

### Step 5: Calculate \(32.5 \times 4\)
Calculating \(32.5 \times 4\):
\[ 32.5 \times 4 = 130 \]

Thus, the value of \(?\) is:
\[ ? = 130 \]

### Final Answer
The value that comes in place of the question mark is \(130\).

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