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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