Two numbers A and B are respectively 10% and 25% more than third number respectively. What is the ratio of A and B?

Options

A. `13:16`
B. `11:12`
C. `22:25`
D. `15:16`

Answer

To solve the problem step by step, we will find the values of A and B based on the information given, and then we will calculate the ratio of A to B.

### Step 1: Define the Third Number
Let the third number be \( C = 100 \).

### Step 2: Calculate A
Since A is 10% more than the third number:
\[ A = C + 10\% \text{ of } C = 100 + 0.10 \times 100 = 100 + 10 = 110 \]

### Step 3: Calculate B
Since B is 25% more than the third number:
\[ B = C + 25\% \text{ of } C = 100 + 0.25 \times 100 = 100 + 25 = 125 \]

### Step 4: Find the Ratio of A to B
Now we need to find the ratio of A to B:
\[ \text{Ratio of } A \text{ to } B = \frac{A}{B} = \frac{110}{125} \]

### Step 5: Simplify the Ratio
To simplify the ratio, we can divide both the numerator and the denominator by 5:
\[ \frac{110 \div 5}{125 \div 5} = \frac{22}{25} \]

### Final Answer
Thus, the ratio of A to B is:
\[ A : B = 22 : 25 \]