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
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Correct Answer: 205
Solution : The ratio of first and second = 3 : 4 = 9 : 12 The ratio of second and third = 3 : 5 = 12 : 20 The ratio of three numbers = 9: 12 : 20 Let the numbers be $9x$, $12x$, and $20x$. Product of first and third = 4500 ⇒ $9x×20x = 4500$ ⇒ $x^2 = \frac{4500}{180}$ = 25 ⇒ $x = 5$ The sum of the three numbers $=9x+12x+20x$ $= 41x$ $= 41 × 5$ $= 205$ Hence, the correct answer is 205.
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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 1: 36
Option 2: 27
Option 3: 63
Option 4: 56
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 2: 30
Option 3: 72
Option 4: 24
Question : The product of two positive numbers is 240. If the ratio of the two numbers is 3 : 5, then what is the sum of the two numbers?
Option 1: 46
Option 2: 45
Option 3: 32
Option 4: 42
Question : Of three positive numbers, the ratio of 1st and 2nd is 8 : 9, and that of 2nd and 3rd is 3 : 4. The product of 1st and 3rd is 2400. The sum of the three numbers is:
Option 1: $45$
Option 2: $85$
Option 3: $95$
Option 4: $55$
Question : Of the three numbers, the first is twice the second, and the second is twice the third. The average of the reciprocal of the numbers is $\frac{7}{12}$. The numbers are:
Option 1: 20, 10 and 5
Option 2: 4, 2 and 1
Option 3: 36, 18 and 9
Option 4: 16, 8 and 4
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