# IQ of a person is given by the formula

Question:

IQ of a person is given by the formula

$\mathrm{IQ}=\frac{\mathrm{MA}}{\mathrm{CA}} \times 100$

Where $M A$ is mental age and $C A$ 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.

Solution:

It is given that for a group of 12 years old children, $80 \leq I Q \leq 140 \ldots$ (i)

For a group of 12 years old children, $\mathrm{CA}=12$ years

$\mathrm{IQ}=\frac{\mathrm{MA}}{12} \times 100$

Putting this value of IQ in (i), we obtain

$80 \leq \frac{\mathrm{MA}}{12} \times 100 \leq 140$

$\Rightarrow 80 \times \frac{12}{100} \leq \mathrm{MA} \leq 140 \times \frac{12}{100}$

$\Rightarrow 9.6 \leq \mathrm{MA} \leq 16.8$

Thus, the range of mental age of the group of 12 years old children is .