Question

P, Q, R and S go for a picnic. When P stands on a weighing machine, Q also climbs on, and the weight shown was 132 kg. When Q stands, R also climbs on, and the machine shows 130 kg. Similarly the weight of R and S is found as 102 kg and that of Q and S is 116 kg. What is Q weight?

• A. 58kg
• B. 78kg
• C. 67kg
• D. 44kg

Answer 1

The Correct Option is C

Let's define the weights of the four people as: 

• P = p
• Q = q
• R = r
• S = s

From the problem statement, we are given the following equations:

\[ p + q = 132 \]

\[ q + r = 130 \]

\[ r + s = 102 \]

\[ q + s = 116 \]

Step 1: Add all the equations

\[ (p+q) + (q+r) + (r+s) + (q+s) = 132 + 130 + 102 + 116 \]

\[ p + 3q + 2r + 2s = 480 \]

Step 2: Express in terms of total weight

From equations (3) and (4):

\[ r + s = 102 \]

\[ q + s = 116 \]

Solving for s:

\[ s = 116 - q \]

Substituting in equation (3):

\[ r + (116 - q) = 102 \]

\[ r = 102 - 116 + q \]

\[ r = q - 14 \]

Step 3: Solve for q

Substituting r = q - 14 in equation (2):

\[ q + (q - 14) = 130 \]

\[ 2q - 14 = 130 \]

\[ 2q = 144 \]

\[ q = 67 \]

Thus, the weight of Q is 67 kg.

Final Answer:

Option (C) 67 kg