In each of the following question and equation is presented in four parts with = sign in between parts. The four parts of the equation are lettered (A) (B) ( C) and (D). One of these parts in the equation may be wrong and there by may not yield the same result as the other three parts do. Find out the wrong part. If there is any. If all the four parts are correctly equated and all of them yield the same result, the answer is (E) i.e.,’No,error’.

Options

A. `10%` of `0cdot12`
B. `12%` of `0cdot1`
C. `1%` of `(12xx0cdot1)`
D. `100%` of `(120xx0cdot00001)`

Answer

To solve the problem, we need to evaluate each of the four parts of the equation to determine if they yield the same result or if one of them is incorrect. The four parts are:

(A) 10% of 0.1
(B) 12% of 0.1
(C) 1% of 12 × 0.1
(D) 100% of 120 × 0.0001

Let's calculate each part step by step.

### Step 1: Calculate Part (A)
**Part (A)**: 10% of 0.1
To calculate this, we convert the percentage to a decimal and multiply:
\[ 10\% = \frac{10}{100} = 0.1 \]
Now, multiply by 0.1:
\[ 0.1 \times 0.1 = 0.01 \]

### Step 2: Calculate Part (B)
**Part (B)**: 12% of 0.1
Convert the percentage to a decimal and multiply:
\[ 12\% = \frac{12}{100} = 0.12 \]
Now, multiply by 0.1:
\[ 0.12 \times 0.1 = 0.012 \]

### Step 3: Calculate Part (C)
**Part (C)**: 1% of 12 × 0.1
First, calculate 1% of 12:
\[ 1\% = \frac{1}{100} = 0.01 \]
Now, multiply by 12:
\[ 0.01 \times 12 = 0.12 \]
Then, multiply by 0.1:
\[ 0.12 \times 0.1 = 0.012 \]

### Step 4: Calculate Part (D)
**Part (D)**: 100% of 120 × 0.0001
Convert the percentage to a decimal and multiply:
\[ 100\% = 1 \]
Now, multiply by 120:
\[ 1 \times 120 = 120 \]
Then, multiply by 0.0001:
\[ 120 \times 0.0001 = 0.012 \]

### Summary of Results
- (A) = 0.01
- (B) = 0.012
- (C) = 0.012
- (D) = 0.012

### Conclusion
From the calculations:
- Part (A) yields 0.01
- Parts (B), (C), and (D) yield 0.012

Thus, the wrong part is **(A)**.