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's weight?

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

Hint:

When multiple equations are given with shared variables, substitute values from one equation into another to simplify and solve step by step.

Answer 1

The Correct Option is C

Let the weights of P, Q, R, and S be \( p \), \( q \), \( r \), and \( s \) respectively. We are given the following equations: \[ p + q = 132 \quad \text{(Equation 1)} \] \[ q + r = 130 \quad \text{(Equation 2)} \] \[ r + s = 102 \quad \text{(Equation 3)} \] \[ q + s = 116 \quad \text{(Equation 4)} \] Step 1: Solve for \( p \) and \( r \) in terms of \( q \). From Equation 1: \[ p = 132 - q \] From Equation 2: \[ r = 130 - q \] Step 2: Substitute \( r = 130 - q \) into Equation 3: \[ 130 - q + s = 102 \] \[ s = 102 - 130 + q \] \[ s = q - 28 \] Step 3: Substitute \( s = q - 28 \) into Equation 4: \[ q + (q - 28) = 116 \] \[ 2q - 28 = 116 \] \[ 2q = 144 \] \[ q = 72 \] Thus, Q's weight is 72 kg.