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
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Correct Answer: 50 and 75
Solution : Given: The two numbers are in the ratio of 2 : 3. Their sum is 125. Let the numbers be $2x$ and $3x$. As per given condition, $2x+3x=125$ ⇒ $5x=125$ ⇒ $x=\frac{125}{5}$ ⇒ $x=25$ So, the numbers are 50 and 75. Hence, the correct answer is 50 and 75.
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Question : The ratio of the two numbers is 3 : 8 and their sum is 88. What is the value of the smaller number?
Option 1: 11
Option 2: 36
Option 3: 64
Option 4: 24
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
Question : Divide 50 into two parts so that the sum of their reciprocal is $\frac{1}{12}$.
Option 1: 35 and 15
Option 2: 20 and 30
Option 3: 24 and 36
Option 4: 28 and 22
Question : The ratio of three positive numbers is 2 : 3 : 5 and the sum of their squares is 608. The three numbers are:
Option 1: 2, 3 and 5
Option 2: 10, 15 and 25
Option 3: 8, 12 and 20
Option 4: 4, 6 and 10
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
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