Question : Three positive numbers are in the ratio of 4 : 5 : 7, and the sum of their squares is 15,210. Find the sum of the three numbers.
Option 1: 148
Option 2: 156
Option 3: 126
Option 4: 208
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Correct Answer: 208
Solution : Let the three positive numbers be 4x, 5x, and 7x. So, (4x) 2 + (5x) 2 + (7x) 2 = 15210 ⇒ 16x 2 + 25x 2 + 49x 2 = 15210 ⇒ 90x 2 = 15210 ⇒ x 2 = 169 $\therefore$ x = 13 Sum of the three numbers = 4x + 5x + 7x = 16x = 16 × 13 = 208 Hence, the correct answer is 208.
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