Question

IQ of a person is given by the formula
$IQ=\frac{MA}{CA}\times100$
where, MA is mental age and CA is chronological age. If $80 \le IQ \le 140$ for a group of 12 years children, then the range of their mental age is

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

Answer 1

Answer: (C)

We have
$IQ=\frac{MA}{CA}\times100$
$\Rightarrow IQ=\frac{MA}{12}\times 100\,\left[\because CA=12\,years\right]$
$=\frac{25}{3}MA$
Given, $80 \le IQ \le 140$
$\Rightarrow 80 \le\frac{25}{3}MA \le 140$
$\Rightarrow 240 \le 25MA \le420$
$\Rightarrow \frac{240}{25} \le mA \le\frac{420}{25}$
$\Rightarrow 9.6 \le MA \le16.8$