Question:

If three numbers are in the ratio 3:2:5 such that the sum of their squares is 1,862, the middle number will be:

Updated On: Oct 14, 2024
  • 7
  • 14
  • 21
  • 35
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The Correct Option is B

Solution and Explanation

The three numbers in the ratio =3:2:53:2:5
The sum of the squares is equal to=18621862.
Ratio of three numbers are =3x:2x:5x3x: 2x: 5x
(3x)2+(2x)2+(5x)2=1862(3x)^{2} + (2x)^{2} + (5x)^{2} = 1862
9x2+4x2+25x2=18629x^{2} + 4x^{2} + 25x^{2} = 1862
x2=186238x^{2}= \frac{1862}{38}
x=49=7x=\sqrt49=7
The middle number is =2×7=142\times7=14
The correct answer is (B): 14

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