Question : The ratio of a two-digit number and the sum of the digits of that number is 4 : 1. If the digit at the unit's place is 3 more than the digit at the ten's place, then the number is:
Option 1: $47$
Option 2: $69$
Option 3: $36$
Option 4: $25$
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Correct Answer: $36$
Solution : Let us assume that the digits of the number are $x$ and $y$ with $x$ in the ten's place. The number is $10x+y$. The digit in the unit's place is 3 more than the digit in the ten's place, i.e. $y=x+3$ ...(1) The ratio between the two-digit number and the sum of the digits of that number is $4 : 1$. $(10x+y):(x+y) = 4:1$ or, $10x+y = 4x+4y$ or, $y = 2x$ Substituting in (1), we get $2x = x+3$ $x = 3, y = 6$ The number is $36$. Hence, the correct answer is $36$.
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Question : The radius of two spheres is in the ratio of 1 : 5. What is the ratio of the volume of the two spheres?
Option 1: 8 : 27
Option 2: 1 : 25
Option 3: 1 : 125
Option 4: 1 : 64
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Option 1: 6
Option 2: 5
Option 3: 4
Option 4: 0
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Option 1: 80
Option 2: 72
Option 3: 85
Option 4: 78
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Option 2: 3
Option 3: 2
Option 4: 4
Question : The difference between the two numbers is 24 while the sum of those two numbers is 120. Which of the options below can be the ratio of those two numbers?
Option 1: 3 : 5
Option 2: 3 : 2
Option 3: 4 : 5
Option 4: 5 : 8
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