Question

The IQ of person is given by the formula, $IQ=\frac{m}{c}\times 100$, where m is the mental age and c is the chromological age. If $80\le IQ\le 140$ for a group of 12-year children, find the range of their mental age.

Answer 1

When $c=12$, we have $IQ=\frac{m}{12}\times 100=\frac{25m}{3}$

$\therefore 80\le IQ\le 140\Rightarrow 80\le \frac{25m}{3}\le 140$

$\Rightarrow 80\le \frac{25m}{3}and\frac{25m}{3}\le 140$

$\Rightarrow \frac{3}{25}\times 80\le mandm\le 140\times \frac{3}{25}$

$\Rightarrow \frac{48}{5}\le mandm\le \frac{84}{5}$

$\Rightarrow 9.6\le m\le 16.8$

Hence, the required mental age for a group of 12-year children is 9.6 years or more and 16.8 years or less.