Three positive numbers are in the ratio 2 : 3 : 4. If the sum of their squares is 2349, the numbers are respectively:

A14, 21 and 28

B18, 27 and 36 ✓ Correct

C16, 24 and 32

D12, 18 and 24

Correct answer: (B) 18, 27 and 36

Explanation

The numbers are 18, 27 and 36.

Let them be 2k, 3k, 4k.

Sum of squares = (4 + 9 + 16)k^2 = 29k^2.

29k^2 = 2349 gives k^2 = 81, so k = 9.

Thus 2k = 18, 3k = 27, 4k = 36.

Ratio terms squared and summed fix the multiplier k.

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