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
Correct Answer: 1 : 1
Solution : Let the numbers be $x$ and $y$. According to the question, $(x + y)^2 = 4xy$ ⇒ $x^2+y^2+2xy-4xy = 0$ ⇒ $x^2+y^2-2xy = 0$ ⇒ $(x -y)^{2} = 0$ ⇒ $x = y$ $\therefore$ The required ratio is 1 : 1. Hence, the correct answer is 1 : 1.
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Question : If the sum of two quantities is equal to three times their difference, then the ratio of the two quantities is:
Option 1: 1 : 3
Option 2: 3 : 1
Option 3: 2 : 1
Option 4: 2 : 3
Question : The product of two numbers is 24 times the difference between these two numbers. If the sum of these numbers is 14, the larger number is:
Option 1: 9
Option 2: 8
Option 3: 7
Option 4: 10
Question : Two numbers are in the ratio 3 : 4. The product of their HCF and LCM is 2700. The sum of the numbers is:
Option 1: 60
Option 2: 105
Option 3: 15
Option 4: 45
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
Question : If the product of three consecutive numbers is 210, then the sum of the 2 smaller numbers is:
Option 1: 3
Option 2: 4
Option 3: 5
Option 4: 11
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