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.

What is the possible weight of S?

The correct option is 53kg.

Let us analyze the given information step-by-step to find the relative order of weights for the six persons: P, Q, R, S, T, and U.

Step 1: Understand the basic statements and conditions

1. There are 6 persons in total.

2. The third heaviest person weighs 40 kg.

3. Q's weight is an odd number. Q is lighter than S but heavier than R: S > Q > R.

4. T is 20 kg more than P: T = P + 20 kg.

5. P is heavier than Q: P > Q.

6. T is heavier than R and U: T > R, T > U.

7. The second lightest person is NOT Q.

Step 2: Determine the positions and relative weights

From the condition "T is 20kg more than P who is heavier than Q", we have:

$T>P>Q$

Also, S > Q > R and P > Q > R.

Notice that P > Q and Q > R. So P > Q > R.

Since T = P + 20 kg, T is clearly the heaviest person or at least heavier than P, Q, R, U.

Let us analyze the condition: "The number of persons lighter than S is one more than P".

Wait, "one more than P" means one more than the number of persons lighter than P.

Let $N\left(X\right)$ be the number of persons lighter than X.

Then $N\left(S\right)=N\left(P\right)+1$.

This means S is positioned directly above P in the weight ranking (S is immediately heavier than P).

So the ordering among T, S, P, Q, R is:

Since T = P + 20, T > S (because S is immediately above P, so S is lighter than P + 20 kg).

Therefore, the weight sequence from heaviest to lightest is:

1. T (Heaviest)

2. S (Second heaviest)

3. P (Third heaviest)

4. Q (Fourth heaviest / Third lightest)

5. U / R (Fifth heaviest / Second lightest)

6. R / U (Lightest)

Let's verify this order:

Persons from 1st (heaviest) to 6th (lightest):

Position 1: T

Position 2: S

Position 3: P (Weight = 40 kg)

Position 4: Q

Position 5: U (since second lightest is not Q, position 5 is U or R)

Position 6: R

Number of persons lighter than P = 3 (Q, U, R).

Number of persons lighter than S = 4 (P, Q, U, R), which is indeed one more than the number of persons lighter than P (3 + 1 = 4).

Step 3: Determine the weight of S

We are given that the 3rd heaviest person (P) weighs 40 kg.

$\text{Weight of P}=40\text{ kg}$

Since T is 20 kg more than P:

$\text{Weight of T}=40+20=60\text{ kg}$

S is between T and P in weight:

$\text{Weight of P}<\text{Weight of S}<\text{Weight of T}$

$40\text{ kg}<\text{Weight of S}<60\text{ kg}$

Looking at the given options:

- 39kg (Less than 40kg - Invalid)

- 34kg (Less than 40kg - Invalid)

- 53kg (Between 40kg and 60kg - Valid)

- 67kg (Greater than 60kg - Invalid)

- 62kg (Greater than 60kg - Invalid)

Therefore, the only possible weight of S from the options is 53kg.