Study the information carefully answer the questions given below.

Six persons P , Q, R, S, T and U in a family have different weights. The third heaviest person weight is 40kg. Q’s weight is in odd number and is lighter than S but heavier than R. The number of persons lighter than S is one more than P . T is heavier than R and U. T is 20kg more than P who is heavier than Q. The second lightest person is not Q.

If R’s weight is 15kg less than P and 5 kg more than U then what is the sum weight of R and U?

The correct option is 45kg.

Let us analyze the given information step-by-step to arrange the six persons (P, Q, R, S, T, U) in decreasing order of their weights:

Step 1: Determine the total number of persons and positions
There are 6 persons. Let the positions from heaviest (1st) to lightest (6th) be:
1st > 2nd > 3rd > 4th > 5th > 6th

Step 2: Position of S and P
We are given:
- "The number of persons lighter than S is one more than P."
Wait, here "one more than P" means one more than the number of persons lighter than P. Let us check the position of S.
- "Q's weight is in odd number and is lighter than S but heavier than R." ⇒ S > Q > R.
- "T is 20kg more than P who is heavier than Q." ⇒ T > P > Q.
So we have: P > Q and S > Q.
Since P > Q > R and T > P > Q > R, we know T, P, Q, R are in order: T > P > Q > R.
Also T is heavier than R and U.
Since P > Q > R, and the second lightest person (5th position) is NOT Q, Q must be heavier than the 5th person, so Q cannot be 5th or 6th. Thus Q must be 4th or higher, but Q is lighter than both S and P/T.
Let us analyze the ordering:
T, P, S are all heavier than Q.
So 3 persons (T, P, S) are heavier than Q. Since there are 6 persons in total, Q must be in the 4th position!
Positions: 1st > 2nd > 3rd > 4th (Q) > 5th > 6th

Since 3 persons (T, P, S) are heavier than Q, the top 3 positions (1st, 2nd, 3rd) are occupied by T, P, and S in some order.
We are given that "The third heaviest person weight is 40kg."
We also know T > P. So P cannot be 1st. Thus T is heavier than P.
- "The number of persons lighter than S is one more than [the number of persons lighter than] P."
If P is 3rd, the number of persons lighter than P is 3. Then persons lighter than S would be 3 + 1 = 4, which means S is 2nd.
Thus, the top 3 positions are:
1st: T
2nd: S
3rd: P (Weight = 40kg)
4th: Q
5th: R (since second lightest is not Q, R is 5th)
6th: U

Let us verify the arrangement:
T > S > P (40kg) > Q > R > U
- 3rd heaviest person is P = 40kg.
- T is 20kg more than P ⇒ T = 40 + 20 = 60kg.
- Persons lighter than P = 3 (Q, R, U). Persons lighter than S = 4 (P, Q, R, U), which is 3 + 1 = 4. This satisfies "number of persons lighter than S is one more than P".
- Second lightest person is R (not Q), which matches the condition.

Step 3: Calculate the weights of R and U based on the question
We are given:
- P's weight = 40kg.
- R's weight is 15kg less than P:

$\text{Weight of R}=40-15=25\text{ kg}$

$\text{Weight of R}=\text{Weight of U}+5$

$25=\text{Weight of U}+5\Rightarrow \text{Weight of U}=20\text{ kg}$

Step 4: Find the sum of weights of R and U

$\text{Sum}=\text{Weight of R}+\text{Weight of U}=25+20=45\text{ kg}$