Answer :
Final answer:
By multiplying each part of the ratio 11:13 by the HCF which is 19, we find the two numbers in question to be 209 and 247. Hence the correct answer is option B
Explanation:
To determine the two numbers that are in the ratio of 11:13 and have a Highest Common Factor (HCF) of 19, we need to use the given information strategically. The HCF of two numbers means that it is the largest number that divides both of them. Since the two numbers are in the proportion 11x to 13x, and their HCF is 19, we can deduce that 'x' must be 19, because the HCF is a factor of both numbers.
Therefore, multiplying each part of the ratio by the HCF:
- 11x = 11 imes 19 = 209
- 13x = 13 imes 19 = 247
Thus, the two numbers are 209 and 247. Option B is the correct answer.
The correct numbers that satisfy the given conditions are 209 and 247.
To find the two numbers, we use the information given:
1. The ratio of the two numbers is [tex]11:13[/tex]. Let's denote the two numbers as 11x and 13x, where x is a common multiplier.
2. The HCF (Highest Common Factor) of these numbers is 19. This means that both numbers are multiples of 19.
Since the HCF is 19, we can express the numbers as [tex]11 * 19[/tex]and [tex]13 * 19[/tex]. This is because the HCF must be a factor of both numbers, and since the ratio of the numbers is [tex]11:13,[/tex] we can directly multiply the HCF by these ratios to get the actual numbers.
Now, let's calculate the numbers:
- For the first number: [tex]11 * 19 = 209[/tex]
- For the second number: [tex]13 * 19 = 247[/tex]
Therefore, the two numbers are 209 and 247.
We can check these numbers against the options provided:
A. 304, 369
B. 209, 247
C. 182, 199
D. 182, 122
The correct pair that matches our calculated numbers is option [tex]B: 209[/tex] and 247. These numbers have the ratio [tex]11:13[/tex] and the HCF of 19, as required by the problem statement.
