Three positive numbers are in the ratio 2 : 3 : 4. The sum of their squares is 2349. The average of the first two numbers is:
Explanation:
Let the three numbers be 2x, 3x and 4x.
⇒ (2x)2 + (3x)2 + (4x)2 = 2349 ⇒ 4x2 + 9x2 + 16x2 = 2349 ⇒ 29x2 = 2349 ⇒ x2 = 81 ⇒ x = 9
∴ The average of first two numbers = (2x + 3x)/2 = 2.5 × 9 = 22.5
Hence, option (d).
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