# IQ of a person is given by the formula $IQ = \dfrac{{MA}}{{CA}} \times 100$ where MA is mental age and CA is chronological age. If $80 \leqslant IQ \leqslant 140$ for a group of 12 year old children, find the range of their mental age.

Answer

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Hint- Chronological age for 12 year old children is 12.

Give that:

For a group of 12 year old children, ${\text{80}} \leqslant IQ \leqslant 140{\text{ }} \ldots \ldots \left( 1 \right)$

$IQ = \dfrac{{MA}}{{CA}} \times 100$

Also, for \[12\] year old children, $CA = 12{\text{ }}\left( {\because {\text{ }}CA{\text{ is chronological age}}} \right)$

Put the value of $IQ$ in equation $\left( 1 \right)$, we get

$

\Rightarrow {\text{80}} \leqslant \dfrac{{MA}}{{CA}} \times 100 \leqslant 140 \\

\Rightarrow {\text{80}} \leqslant \dfrac{{MA}}{{12}} \times 100 \leqslant 140{\text{ }}\left( {\because {\text{ }}CA = 12} \right) \\

$

Multiply by $12$ and divide by $100$ on each side of inequality, we get

$

\Rightarrow \dfrac{{{\text{80}} \times {\text{12}}}}{{100}} \leqslant MA \leqslant \dfrac{{140 \times 12}}{{100}} \\

\Rightarrow 9.6 \leqslant MA \leqslant 16.8 \\

$

$\ therefore $ The range of mental age for group $12$ year old children is $9.6 \leqslant MA \leqslant 16.8$

Note- Whenever you see a problem like this, always try to make algebraic equations using given information from the question and solve them using simple algebraic calculations.

Give that:

For a group of 12 year old children, ${\text{80}} \leqslant IQ \leqslant 140{\text{ }} \ldots \ldots \left( 1 \right)$

$IQ = \dfrac{{MA}}{{CA}} \times 100$

Also, for \[12\] year old children, $CA = 12{\text{ }}\left( {\because {\text{ }}CA{\text{ is chronological age}}} \right)$

Put the value of $IQ$ in equation $\left( 1 \right)$, we get

$

\Rightarrow {\text{80}} \leqslant \dfrac{{MA}}{{CA}} \times 100 \leqslant 140 \\

\Rightarrow {\text{80}} \leqslant \dfrac{{MA}}{{12}} \times 100 \leqslant 140{\text{ }}\left( {\because {\text{ }}CA = 12} \right) \\

$

Multiply by $12$ and divide by $100$ on each side of inequality, we get

$

\Rightarrow \dfrac{{{\text{80}} \times {\text{12}}}}{{100}} \leqslant MA \leqslant \dfrac{{140 \times 12}}{{100}} \\

\Rightarrow 9.6 \leqslant MA \leqslant 16.8 \\

$

$\ therefore $ The range of mental age for group $12$ year old children is $9.6 \leqslant MA \leqslant 16.8$

Note- Whenever you see a problem like this, always try to make algebraic equations using given information from the question and solve them using simple algebraic calculations.

Last updated date: 26th Sep 2023

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