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Questions  >>  CBSE XI  >>  Math  >>  Linear Inequalities

Ravi obtained 70 and 75 marks in first two unit tests. Find the minimum marks he should get in third test to have an average of at least 60 marks.

$\begin{array}{1 1} (A)\;78 \\(B)\;35 \\(C)\;56 \\(D)\;20 \end{array} $

1 Answer

  • Same Quantity can be added (a subtracted ) to (from ) both sides of the inequality with out changing the sign of the in equality.
  • Same positive quantities can be multiplied or divided to both side of the in equality with out changing the sign of the inequality.
  • If same negative quantity is multiplied or divided to both sides of the inequality is reversed i.e $ '>'$ sign changes to $'<' $ and $'<'$ changes $'>'$ .
Let x be the mark Ravi obtained in the third unit test.
Total marks obtained in the three test is $70+75+x$
Since the average marks of the three test in at least 60 $\large\frac{70 +75+x}{3} $$ \geq 60$
Multiplying both sides of inequality by 3 .
$145 + x \geq 180$
Subtracting 145 from both sides of the inequality.
$x \geq 180-145$
$x \geq 35$
Step 2:
The student must obtain a minimum mark of 35 to get an average of 60 marks.
Hence B is the correct answer.
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