Question : The difference between 24 and the mean proportional of 7 and 63 is:
Option 1: 3
Option 2: 2
Option 3: 5
Option 4: 4
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Correct Answer: 3
Solution : Let $x$ be the mean proportion. $a=7,b=63$ For mean proportion: $\frac{a}{x}=\frac{x}{b}$ $⇒x^2 = a\times{b}$ $⇒x = \sqrt{7\times63}$ $⇒ x = \sqrt{441}$ $⇒x = 21$ $\therefore$ The difference between 24 and the mean proportional of 7 and 63 is $=24-21 = 3$ Hence, the correct answer is 3.
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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
Question : What is the mean proportional between 3 and 27?
Option 1: 30
Option 2: 81
Option 3: 15
Option 4: 9
Question : The value of $\frac{3+8 \times 8 \div 8 \text { of } 8+7 \div 7 \times 2}{5 \div 5 \text { of } 4+3 \times 3 \div 3-3+2}$ is:
Option 1: $1 \frac{3}{5}$
Option 2: $2 \frac{2}{3}$
Option 3: $1 \frac{4}{7}$
Option 4: $2 \frac{3}{7}$
Question : The sum of the two numbers is 37 and the difference between their squares is 185, then the difference between the two numbers is:
Option 1: 10
Option 2: 4
Option 4: 3
Question : If the difference between the two numbers is 20 percent of their sum, then what is the ratio of larger number and smaller number?
Option 1: 6 : 5
Option 2: 5 : 4
Option 3: 4 : 3
Option 4: 3 : 2
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