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Ratio of the ages of three persons A, B, C is 3 : 5 : 4. Sum of the squares of A and B is equal to 68 times of C age. Find the difference between A and B ages

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Detailed Solution

$A : B : C = 3 : 5 : 4$

$A^{2} + B^{2} = 68 C \dots (1)$

$9 X^{2} + 25 X^{2} = 68 \times 4 X$

$34 X^{2} = 68 \times 4 X$

X=8

difference between A and B ages=5X-3X=2X=2 $\times 8 = 16$

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