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Ratio of two numbers is 3 : 5. If x is added to each, the new ratio is 7 : 5. Sum of squares of the original numbers in terms of x is:
Answer & Solution
Correct answer: D.
1. Let numbers = 3k, 5k. After adding x: (3k+x)/(5k+x) = 7/5 → 5(3k+x) = 7(5k+x) → 15k+5x = 35k+7x → −20k = 2x → k = −x/10. (Negative k indicates sign convention; we take absolute value for sum of squares).
2. Sum of squares = (3k)² + (5k)² = 9k² + 25k² = 34k².
3. k² = x²/100. So sum = 34 · x²/100 = 34x²/100 = 17x²/50.
4. Answer: 17x²/50.
_Source: TSICET 2024 PYQ Q.79 (Shift 1, Ratio and Proportion)_
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