Answer :
To solve this problem, we're given that two numbers are in the ratio of 15:11 and that their highest common factor (HCF) is 13. We need to find the actual numbers.
1. Understanding Ratios: ratios are a way to compare two quantities. Here, the numbers are in the ratio of 15:11. This means if the first number is 15 parts, the second number is 11 parts of the same kind.
2. Using the HCF: The highest common factor (HCF) of two numbers is the largest number that divides both of them without leaving a remainder. Here, we are given that the HCF is 13.
3. Formulating the Numbers: Let's denote the two numbers as 15x and 11x based on their ratio. The 'x' here represents a common multiple that, when combined with the ratio, gives the actual numbers.
4. Using the HCF Condition: Since the HCF of these two numbers is 13, we multiply each part of the ratio by 13 to find the actual numbers. Thus:
- The first number becomes: [tex]\(15 \times 13 = 195\)[/tex]
- The second number becomes: [tex]\(11 \times 13 = 143\)[/tex]
5. Conclusion: Therefore, the two numbers are 195 and 143, respectively.
So, the correct answer is option (A) 195 and 143.
1. Understanding Ratios: ratios are a way to compare two quantities. Here, the numbers are in the ratio of 15:11. This means if the first number is 15 parts, the second number is 11 parts of the same kind.
2. Using the HCF: The highest common factor (HCF) of two numbers is the largest number that divides both of them without leaving a remainder. Here, we are given that the HCF is 13.
3. Formulating the Numbers: Let's denote the two numbers as 15x and 11x based on their ratio. The 'x' here represents a common multiple that, when combined with the ratio, gives the actual numbers.
4. Using the HCF Condition: Since the HCF of these two numbers is 13, we multiply each part of the ratio by 13 to find the actual numbers. Thus:
- The first number becomes: [tex]\(15 \times 13 = 195\)[/tex]
- The second number becomes: [tex]\(11 \times 13 = 143\)[/tex]
5. Conclusion: Therefore, the two numbers are 195 and 143, respectively.
So, the correct answer is option (A) 195 and 143.
