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  4. IQ of a person is given by the formula IQ =( MA / CA ) × 100 where, MA is mental age and CA is chronological age. If 80 ≤ IQ ≤ 140 for a group of 12 years children, then the range of their mental age is

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Q. IQ of a person is given by the formula
$IQ =\frac{ MA }{ CA } \times 100$
where, $MA$ is mental age and $CA$ is chronological age. If $80 \leq IQ \leq 140$ for a group of $12$ years children, then the range of their mental age is

Linear Inequalities

Solution:

We have IQ $=\frac{\text { MA }}{\text { CA }} \times 100$
$\Rightarrow IQ =\frac{\text { MA }}{12} \times 100=\frac{25}{3}$ MA
$[\because$ CA $=12$ years $]$
Given, $80 \leq I Q \leq 140 $
$\Rightarrow 80 \leq \frac{25}{3}$ MA $\leq 140$
$\Rightarrow 240 \leq 25 MA \leq 420$
$ \Rightarrow \frac{240}{25} \leq MA \leq \frac{420}{25}$
$\Rightarrow 9.6 \leq MA \leq 16.8$