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CAT 2015 | Question: 95

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Given that, equation $2x+y = 40$

$\Rightarrow \boxed{y= 40-2x ; x \le y \longrightarrow (1)}$

Put the various values of $x$ in equation $(1),$ and get the number of solutions.

  • $x=1 \Rightarrow y=38$
  • $x=2 \Rightarrow y=36$
  • $x=3 \Rightarrow y=34$
  • $x=4 \Rightarrow y=32$
  • $x=5 \Rightarrow y=30$
  • $x=6 \Rightarrow y=28$
  • $x=7 \Rightarrow y=26$
  • $x=8 \Rightarrow y=24$
  • $x=9 \Rightarrow y=22$
  • $x=10 \Rightarrow y=20$
  • $x=11 \Rightarrow y=18$
  • $x=12 \Rightarrow y=16$
  • $x=13 \Rightarrow y=14$
  • $x=14 \Rightarrow y=12$ $(x \le y)$ Conditions Violated

$\therefore$ The number of solutions of the equation $2x+y=40$ is $13.$

Correct Answer $: 13$

 

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