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IQ of a person is given by the formula $I Q=\frac{M A}{C A} \times 100$
Where MA is mental age and $\mathrm{CA}$ is chronological age. If $80 \leq I Q \leq 140$ for a group of 12 years old children, find the range of their mental age.
Where MA is mental age and $\mathrm{CA}$ is chronological age. If $80 \leq I Q \leq 140$ for a group of 12 years old children, find the range of their mental age.
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We have $\mathrm{IQ}=\frac{\mathrm{MA}}{\mathrm{CA}} \times 100$
We are given $80 \leq \mathrm{IQ} \leq 140$
Putting the value of IQ in it,
$80 \leq \frac{\mathrm{MA}}{\mathrm{CA}} \times 100 \leq 140$
Since, $\mathrm{CA}=12$ therefore,
Multiplying by 12 , we get
$\begin{aligned}
& 12 \times 80 \leq \mathrm{MA} \times 100 \leq 140 \times 12 \\
\Rightarrow & 960 \leq 100 \mathrm{MA} \leq 1680
\end{aligned}$
Dividing by $100 ; \quad 9.6 \leq \mathrm{MA} \leq 16.8$
Hence, mental age is greater than or equal to $9.6$ and less than or equal to $16.8$ years.
We are given $80 \leq \mathrm{IQ} \leq 140$
Putting the value of IQ in it,
$80 \leq \frac{\mathrm{MA}}{\mathrm{CA}} \times 100 \leq 140$
Since, $\mathrm{CA}=12$ therefore,
Multiplying by 12 , we get
$\begin{aligned}
& 12 \times 80 \leq \mathrm{MA} \times 100 \leq 140 \times 12 \\
\Rightarrow & 960 \leq 100 \mathrm{MA} \leq 1680
\end{aligned}$
Dividing by $100 ; \quad 9.6 \leq \mathrm{MA} \leq 16.8$
Hence, mental age is greater than or equal to $9.6$ and less than or equal to $16.8$ years.
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