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 numbers are in the ratio of 3 : 5. if their HCF is 11, then find the sum of two numbers.
Option 1: 55
Option 3: 53
Option 4: 88
Question : The sum of the two numbers is 45. Their HCF and LCM are 5 and 70 respectively. Find the sum of the reciprocal of the two numbers.
Option 1: $\frac{9}{70}$
Option 2: $\frac{3}{140}$
Option 3: $\frac{4}{35}$
Option 4: $\frac{3}{16}$
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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