Question : Find 2 numbers such that their mean proportional is 25 and their third proportional is 25.
Option 1: 5 and 5
Option 2: 5 and 25
Option 3: 25 and 125
Option 4: 25 and 25
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Correct Answer: 25 and 25
Solution : Let, the two numbers be $x$ and $y$, respectively. The mean proportional between $x$ and $y$ is 25. $x:25=25:y$ ⇒ $xy=625$ The third proportional to $x$ and $y$ is 25. $x:y=y:25$ ⇒ $y^2=25x$ ⇒ $y^2=25×\frac{625}{y}$ ⇒ $y^3=25×625=15625=25$ $∴y=25$ Now, $x=\frac{625}{y}=25$ So, the two numbers are 25 and 25, respectively. Hence, the correct answer is 25 and 25.
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Question : Find two numbers such that their mean proportion is 16 and the third proportion is 1024.
Option 1: 4 and 32
Option 2: 4 and 64
Option 3: 8 and 64
Option 4: 8 and 32
Question : Find the third proportional to 8 and 20.
Option 1: 25
Option 2: 50
Option 3: 40
Option 4: 64
Question : Find the third proportional of 25 and 45.
Option 1: 85
Option 2: 65
Option 3: 81
Option 4: 76
Question : Two numbers are in the ratio of 2 : 3. If their sum is 125, find the numbers.
Option 1: 50 and 75
Option 2: 24 and 36
Option 3: 20 and 30
Option 4: 32 and 78
Question : Two positive whole numbers are such that the sum of the first number and twice the second number is 8, and their difference is 2. The numbers are:
Option 1: 7 and 5
Option 2: 6 and 4
Option 3: 4 and 2
Option 4: 3 and 5
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