CDS 2025 · PYQ · Ratio and Proportion · easy
If (x + y) : (y + z) : (z + x) = 3 : 5 : 6 and x + y + z = 14, then what is x² + y² + z² equal to?
- A.81
- B.84✓ Correct
- C.87
- D.90
Let x+y = 3k, y+z = 5k, z+x = 6k. Sum: 2(x+y+z) = 14k, so x+y+z = 7k = 14, k = 2. Then x+y = 6, y+z = 10, z+x = 12. Solving: z = 14 - 6 = 8, x = 14 - 10 = 4, y = 14 - 12 = 2. So x²+y²+z² = 16 + 4 + 64 = 84.
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