Directions: Read the following information carefully and answer the question given below.

Six individuals—P, Q, R, S, T, and U—are of different heights. P is the second tallest person among them. Exactly two people are shorter than P but taller than R. Q is immediately taller than S. T is taller than Q. The height of the second tallest person is 180 cm.

If the combined height of P and S is 330 cm and the height of U is 120 cm, what is the sum of the heights of U and S?

The correct option is 270 cm.

Step-by-Step Explanation:

Step 1: Determine the height arrangement of the six individuals
We are given six individuals: P, Q, R, S, T, and U. Let us order them from tallest (1st) to shortest (6th):
1. "P is the second tallest person among them." So, P is at position 2.
2. "The height of the second tallest person is 180 cm." Therefore, Height of P = 180 cm.
3. "Exactly two people are shorter than P but taller than R." Since P is at position 2, the positions shorter than P are 3, 4, 5, and 6. The two individuals shorter than P but taller than R must occupy positions 3 and 4, which places R at position 5.
4. "Q is immediately taller than S." This means Q and S are adjacent, with Q placed directly above S.
5. "T is taller than Q." Thus, the height order is T > Q > S. Placing T at position 1, Q at position 3, and S at position 4 satisfies all given conditions.
6. The remaining person, U, occupies position 6 (shortest).

The position arrangement from tallest to shortest is:
1st: T
2nd: P (180 cm)
3rd: Q
4th: S
5th: R
6th: U

Step 2: Find the height of S
We are given that the combined height of P and S is 330 cm:

$\text{Height of P}+\text{Height of S}=330\text{cm}$

Substitute the height of P (180 cm) into the equation:

$180+\text{Height of S}=330$

$\text{Height of S}=330-180=150\text{cm}$

Step 3: Calculate the sum of the heights of U and S
We are given that the height of U is 120 cm. Now we add the heights of U and S:

$\text{Sum}=\text{Height of U}+\text{Height of S}$

$\text{Sum}=120+150=270\text{cm}$

Thus, the sum of the heights of U and S is 270 cm.