Six family members P, Q, R, S, T, and U have different weights. The third heaviest person weighs 40 kg. Q's weight is an odd number and Q is lighter than S but heavier than R. The number of people lighter than S is one more than the number of people lighter than P. T is heavier than both R and U. T weighs 20 kg more than P, who is heavier than Q. The second lightest person is not Q.

If R's weight is 15 kg less than P and 5 kg more than U, what is the sum of the weights of R and U?

Question

Six family members P, Q, R, S, T, and U have different weights. The third heaviest person weighs 40 kg. Q's weight is an odd number and Q is lighter than S but heavier than R. The number of people lighter than S is one more than the number of people lighter than P. T is heavier than both R and U. T weighs 20 kg more than P, who is heavier than Q. The second lightest person is not Q.

If R's weight is 15 kg less than P and 5 kg more than U, what is the sum of the weights of R and U?

Accepted Answer

**Solution:** 1. Let us denote the weights of the six persons as follows: - P = p kg - Q = q kg - R = r kg - S = s kg - T = t kg - U = u kg 2. Given that the third heaviest person weighs 40 kg. 3. Q's weight is an odd number, and Q is lighter than S but heavier than R: $$r < q < s$$ 4. The number of persons lighter than S is one more than the number lighter than P: $$ ext{#lighter than } S = ext{#lighter than } P + 1$$ 5. T is heavier than R and U: $$t > r, t > u$$ 6. T is 20 kg heavier than P: $$t = p + 20$$ 7. P is heavier than Q: $$p > q$$ 8. The second lightest person is not Q. 9. Given: - $$r = p - 15$$ - $$r = u + 5 ightarrow u = r - 5$$ 10. Since T is the heaviest (because T > R, U and T = p + 20), and the third heaviest weighs 40 kg, we can arrange weights in descending order: Let's assume the order from heaviest to lightest is: $$T > S > ext{third heaviest} = 40 ext{ kg} > ext{fourth} > ext{fifth} > ext{sixth}$$ 11. Since the third heaviest weighs 40 kg, and T is heaviest, S is second heaviest, so the third heaviest must be P or Q or R or U. 12. Since P is heavier than Q, and Q is heavier than R, and R is heavier than U, and T is heaviest, S is second heaviest, the order is: $$T > S > P > Q > R > U$$ 13. The third heaviest is P, so: $$p = 40 ext{ kg}$$ 14. From (9), $$r = p - 15 = 40 - 15 = 25 ext{ kg}$$ $$u = r - 5 = 25 - 5 = 20 ext{ kg}$$ 15. The sum of weights of R and U is: $$r + u = 25 + 20 = 45 ext{ kg}$$ **Answer:** 45 kg

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