Question

Among 5 objects P, Q, R, S and T

i. R is twice as heavy as T
ii. S is one and half times as heavy as Q
iii. Q and R together weigh as much as S and T together
iv. P and S together are one and half time as heavy as Q and T together
Which among the five is the heaviest of all?
A. Q
B. S
C. P
D. R​

Answer 1

After analyzing the information step by step, using algebraic expressions to represent the relationships between the masses of the objects, it is determined that S is the heaviest object among P, Q, R, S, and T.

Step-by-step explanation:

To determine which of the five objects (P, Q, R, S, T) is the heaviest, we need to analyze the given information step by step.

1. R is twice as heavy as T: R = 2T
2. S is one and a half times as heavy as Q: S = 1.5Q
3. Q and R together weigh as much as S and T together: Q + R = S + T
4. P and S together are one and a half times as heavy as Q and T together: P + S = 1.5(Q + T)

Let's represent the masses in terms of the mass of T, since we have a direct comparison between R and T.

• Substitute R as 2T into the third equation: Q + 2T = S + T
• Rearrange to find Q: Q = S - T
• Substitute Q in terms of S and T into the fourth equation: P + S = 1.5(S - T + T)
• Simplify the equation to find P: P + S = 1.5S or P = 0.5S

Now that we have expressions for P, Q, and R in terms of S and T, we can see that P is half the mass of S, Q is less than S (since Q is S minus something), and R is twice T, but we don't have explicit information about S and T to compare directly. However, since R is dependent on T and T is not the heaviest (otherwise R would have to be heavier than S, but it cannot be per information iii), and P is less than S, it appears that S is the heaviest of all: Option B.