Question : Two numbers are in the ratio 7 : 11. If their HCF is 28, then the sum of the two numbers is:
Option 1: 504
Option 2: 196
Option 3: 308
Option 4: 112
Correct Answer: 504
Solution : If two numbers are in the ratio 7 : 11, then the numbers as $7x$ and $11x$, where $x$ is a common factor. Given that their highest common factor (HCF) is 28. Such that $x = 28$. So, the two numbers are 7 × 28 = 196 and 11 × 28 = 308. Therefore, the sum of the two numbers is 196 + 308 = 504. Hence, the correct answer is 504.
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Question : Two numbers are in the ratio 7 : 11. If their HCF is 28, then the difference between the two numbers is:
Option 1: 28
Option 2: 308
Option 3: 112
Option 4: 196
Question : If the sum of two numbers is 60 and their HCF and LCM are 5 and 60, respectively, then the sum of the reciprocals of the numbers will be:
Option 1: $\frac{1}{11}$
Option 2: $\frac{1}{6}$
Option 3: $\frac{1}{4}$
Option 4: $\frac{1}{5}$
Question : If the square of the sum of two numbers is equal to 4 times their product, then the ratio of these numbers is:
Option 1: 2 : 1
Option 2: 1 : 3
Option 3: 1 : 1
Option 4: 1 : 2
Question : If three numbers are in the ratio of 1 : 3 : 7, and their LCM is 336, then their HCF is:
Option 1: 16
Option 2: 18
Option 3: 10
Option 4: 12
Question : The ratio of the two numbers is 5 : 7 and their HCF is 3. Their LCM is:
Option 1: 75
Option 2: 105
Option 3: 125
Option 4: 35
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