12 of 26% of `5/(78)` of 38% of `7/(152)` of 10000= ?

Options

A. 38
B. 35
C. 41
D. 52

Answer

To solve the question step by step, we will break down the expression provided:

**Question:**
12 of 26% of \( \frac{5}{78} \) of 38% of \( \frac{7}{152} \) of 10000 = ?

### Step 1: Convert percentages to fractions
We know that "A percent" can be written as \( \frac{A}{100} \). Therefore, we convert 26% and 38%:

- 26% = \( \frac{26}{100} \)
- 38% = \( \frac{38}{100} \)

### Step 2: Rewrite the expression
Now we can rewrite the expression using multiplication:

\[ 12 \times \frac{26}{100} \times \frac{5}{78} \times \frac{38}{100} \times \frac{7}{152} \times 10000 \]

### Step 3: Simplify the expression
Now, we can simplify the expression step by step:

1. Combine the fractions:
\[ = 12 \times \frac{26 \times 5 \times 38 \times 7 \times 10000}{100 \times 100 \times 78 \times 152} \]

2. Calculate the denominator:
\[ = 12 \times \frac{26 \times 5 \times 38 \times 7 \times 10000}{10000 \times 78 \times 152} \]

### Step 4: Cancel out common terms
We can cancel \( 10000 \) in the numerator and denominator:
\[ = 12 \times \frac{26 \times 5 \times 38 \times 7}{78 \times 152} \]

### Step 5: Simplify further
Now we can simplify \( \frac{26}{78} \) and \( \frac{38}{152} \):

1. \( \frac{26}{78} = \frac{1}{3} \)
2. \( \frac{38}{152} = \frac{1}{4} \)

Substituting these values back into the expression:
\[ = 12 \times \frac{1}{3} \times 5 \times \frac{1}{4} \times 7 \]

### Step 6: Calculate the remaining expression
Now we can calculate:
\[ = 12 \times \frac{5 \times 7}{3 \times 4} \]
\[ = 12 \times \frac{35}{12} \]

### Step 7: Final calculation
The \( 12 \) in the numerator and denominator cancels out:
\[ = 35 \]

### Final Answer:
The final answer is \( 35 \).

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