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)

$9.6 \le MA \le 16.8$

Answer 2

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, $80 \le IQ \le 140$ $\Rightarrow 80 \le\frac{25}{3}MA \le 140$ $\Rightarrow 240 \le 25MA \le420$ $\Rightarrow \frac{240}{25} \le mA \le\frac{420}{25}$ $\Rightarrow 9.6 \le MA \le16.8$