Question : Three numbers are in the ratio 4 : 5 : 7. The sum of the smallest and largest numbers is 44. What is the second smallest number?
Option 1: 28
Option 2: 32
Option 3: 20
Option 4: 24
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Correct Answer: 20
Solution : Given: The sum of the smallest and largest numbers is 44. Let the three numbers be $4x, 5x,$ and $7x$. The sum of the smallest and the largest numbers is 44. ⇒ $4x+7x=44$ ⇒ $11x=44$ ⇒ $x=4$ $\therefore$ The second smallest number $= 5x=5\times4=20$ Hence, the correct answer is 20.
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Question : Three numbers are in the ratio 2 : 5 : 7. The sum of the smallest and largest number equals the sum of the second number and 16. What is the smallest number?
Option 1: 8
Option 2: 12
Option 3: 6
Option 4: 10
Question : Three numbers are in the ratio of 1 : 2 : 3. The product of the three numbers is 1296. What is the sum of the three numbers?
Option 1: 36
Option 2: 30
Option 3: 72
Question : The sum of three numbers is 126. If the ratio of the first to third is 3 : 7 and that of the second to third is 4 : 7, then what is the second number?
Option 2: 27
Option 3: 63
Option 4: 56
Question : In three positive numbers, the ratio of first and second is 3 : 4 and the ratio of second and third is 3 : 5. The product of first and third is 4500. What is the sum of the three numbers?
Option 1: 282
Option 2: 235
Option 3: 198
Option 4: 205
Question : If 20% of a number is $\frac{1}{6}$th of another number, what is the ratio of the first number to the second number?
Option 1: 4 : 7
Option 2: 5 : 6
Option 3: 5 : 3
Option 4: 4 : 5
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