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Questions  >>  CBSE XI  >>  Math  >>  Linear Inequalities
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Q)

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} $

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A)
Toolbox:
  • 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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