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Two numbers A and B are, respectively, 2...

Two numbers A and B are, respectively, 20% and 56% more than a third number C. The ratio of the numbers A to B is:

A

`10:13`

B

`10:17`

C

`11:13`

D

`7:11`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to find the ratio of two numbers A and B, which are given as percentages more than a third number C. ### Step-by-Step Solution: 1. **Define the Third Number C**: Let's assume the value of the third number C is 100. This simplifies our calculations since we will be working with percentages. 2. **Calculate A**: A is 20% more than C. \[ A = C + 20\% \text{ of } C = 100 + 20\% \text{ of } 100 = 100 + 20 = 120 \] 3. **Calculate B**: B is 56% more than C. \[ B = C + 56\% \text{ of } C = 100 + 56\% \text{ of } 100 = 100 + 56 = 156 \] 4. **Find the Ratio of A to B**: Now we can find the ratio of A to B. \[ \text{Ratio of A to B} = \frac{A}{B} = \frac{120}{156} \] 5. **Simplify the Ratio**: To simplify the ratio, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 120 and 156 is 12. \[ \frac{120 \div 12}{156 \div 12} = \frac{10}{13} \] 6. **Final Answer**: Thus, the ratio of A to B is \( \frac{10}{13} \).
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