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GATE 2018 CE (CE1) – Question 5

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

Room temperature obeys $T=K(\Theta p+T_0)$, where $T_0$ is outside temperature, p number of occupants, and K, Θ constants. Data $(T_0,p,T)$ are (25,2,32.4) and (30,5,42.0). Find Θ.

  1. 0.8
  2. 1.0
  3. 2.0
  4. 10.0

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Correct answer: (B) 1.0

Explanation

The rows give $32.4=K(2\Theta+25)$ and $42=K(5\Theta+30)$. Divide the equations and cross-multiply: $42(2\Theta+25)=32.4(5\Theta+30)$. Hence $78\Theta=78$, so Θ = 1.0 (B).