Question : Three positive numbers are in the proportion of 2 : 3 : 5. If the sum of their squares is 342, then find the largest number.
Option 1: 35
Option 2: 55
Option 3: 15
Option 4: 25
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Correct Answer: 15
Solution : Let the numbers be $2x,3x$ and $5x$. According to the question, $4x^2+9x^2+25x^2=342$ ⇒ $38x^2=342$ ⇒ $x^2=9$ ⇒ $x=3$ Thus, the largest number is $5x=5\times3=15$ Hence, the correct answer is 15.
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Question : The sum of the squares of 3 consecutive positive numbers is 365. The sum of the numbers is:
Option 1: 30
Option 2: 33
Option 3: 36
Option 4: 45
Question : The sum of squares of 3 consecutive positive numbers is 365. The sum of the numbers is:
Question : The LCM of the two numbers is 4 times their HCF. The sum of LCM and HCF is 125. If one of the numbers is 100, then the other number is:
Option 1: 5
Option 2: 25
Option 3: 100
Option 4: 125
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 : Three numbers, a, b, and c are said to be in continued proportion if a : b :: b : c. What number must be added to each of the numbers 1, 7 and 25 so that the resulting sums, in that order, maybe in continued proportion?
Option 1: 2
Option 2: 4
Option 3: 6
Option 4: 5
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