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 $80\le IQ\le 140$ 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 $=\frac{\text{ MA }}{\text{ CA }}\times 100$
$\Rightarrow IQ=\frac{\text{ MA }}{12}\times 100=\frac{25}{3}$ MA
$[\because$ CA $=12$ years $]$
Given, $80\le IQ\le 140$
$\Rightarrow 80\le \frac{25}{3}$ MA $\le 140$
$\Rightarrow 240\le 25MA\le 420$
$\Rightarrow \frac{240}{25}\le MA\le \frac{420}{25}$
$\Rightarrow 9.6\le MA\le 16.8$