Question

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 $12 yr$ children, then the range of their mental age is

• A. $9.8 \leq MA \leq 16.8$
• B. $10 \leq M A \leq 16$
• C. $9.6 \leq MA \leq 16.8$
• D. $9.6 \leq M A \leq 16.6$

Answer 1

Answer: (C)

We have,
$ IQ =\frac{M A}{C A} \times 100 $
$\Rightarrow IQ =\frac{M A}{12} \times 100 $ $(\because CA =12 yr )$
$ =\frac{25}{3} MA$
Given, $ 80 \leq 1 Q \leq 140 $
$\Rightarrow 80 \leq \frac{25}{3} M A \leq 140 $
$ \Rightarrow 240 \leq 25 M A \leq 420 $
$ \Rightarrow \frac{240}{25} \leq M A \leq \frac{420}{25}$
$\Rightarrow 9.6 \leq M A \leq 16.8$