If the product of 15% of 15% and 10% of a number is 250.Find the sum of the 15% and 10%of that number

Options

A. `83.33`
B. `41.65`
C. `41.66`
D. `42.54`

Answer

To solve the problem step by step, we will follow the instructions given in the video transcript.

### Step 1: Define the variables
Let the unknown number be represented by \( x \).

### Step 2: Calculate 15% of 15%
15% can be expressed as a fraction:
\[ 15\% = \frac{15}{100} = \frac{3}{20} \]
Now, we need to find 15% of 15%:
\[ 15\% \text{ of } 15\% = \frac{3}{20} \times \frac{3}{20} = \frac{9}{400} \]

### Step 3: Calculate 10% of the number
10% can also be expressed as a fraction:
\[ 10\% = \frac{10}{100} = \frac{1}{10} \]
Thus, 10% of the number \( x \) is:
\[ 10\% \text{ of } x = \frac{1}{10} x \]

### Step 4: Set up the equation
According to the problem, the product of 15% of 15% and 10% of the number is equal to 250:
\[ \frac{9}{400} \times \frac{1}{10} x = 250 \]

### Step 5: Simplify the equation
Now, simplify the left side:
\[ \frac{9}{4000} x = 250 \]

### Step 6: Solve for \( x \)
To isolate \( x \), multiply both sides by \( 4000 \):
\[ 9x = 250 \times 4000 \]
Calculating the right side:
\[ 250 \times 4000 = 1000000 \]
Now, divide both sides by 9:
\[ x = \frac{1000000}{9} \approx 111111.11 \]

### Step 7: Calculate 15% and 10% of \( x \)
Now, we need to find 15% and 10% of \( x \):
1. **15% of \( x \)**:
\[ 15\% \text{ of } x = \frac{3}{20} \times \frac{1000000}{9} = \frac{30000000}{180} = \frac{166666.67}{1} \approx 166666.67 \]

2. **10% of \( x \)**:
\[ 10\% \text{ of } x = \frac{1}{10} \times \frac{1000000}{9} = \frac{100000}{9} \approx 11111.11 \]

### Step 8: Find the sum of 15% and 10% of \( x \)
Now, we add the two results:
\[ \text{Sum} = 166666.67 + 11111.11 \approx 177777.78 \]

### Final Answer
The sum of 15% and 10% of the number is approximately \( 177777.78 \).

---