65. IQ of a person is given by the formula IQ=MACA*100, where MA is mental age and CA is chronological age. If 80 ≤IQ ≤140 for a group of 12 years old child, find the range of their mental age.

It is given that, IQ = MACA*100…. (1) and 80 ≤ IQ ≤ 140 ⇒−3−4 ……. (2) Putting (1) in (2) we get, 80, MACA*100, 140. Let x be the mental age for chronological age 12, then we can write, 80, x12*100, 140. ⇒ 80*12100≤x12*100*12100≤140*12100 (multypling by 12/1200 throughout) ⇒ 9.6≤x≤16.8. ∴ x∈ [9.6, 16.8] Thus, the required metal age for 12 yes old children is from 9.6 to 16.8.

65. IQ of a person is given by the formula

$I Q = \frac{M A}{C A} * 100,$

where MA is mental age and CA is chronological age. If 80 $\leq$ IQ $\leq$ 140 for a group of 12 years old child, find the range of their mental age.

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Payal Gupta | Contributor-Level 10

9 months ago

It is given that,

IQ = $\frac{MA}{C A} * 100$ …. (1)

and 80 $\leq$ IQ $\leq$ 140 $\Rightarrow - 3 - 4$ ……. (2)

Putting (1) in (2) we get,

$8 0,$
$\frac{M A}{C A} * 10 0, 140 .$

Let x be the mental age for chronological age 12, then we can write,

$8 0,$
$\frac{x}{12} * 10 0, 140 .$

$\Rightarrow 80 * \frac{12}{100} \leq \frac{x}{12} * 100 * \frac{12}{100} \leq 140 * \frac{12}{100}$ (multypling by 12/1200 throughout)

$\Rightarrow 9.6 \leq x \leq 16.8 .$

$∴ x \in [9.6, 16.8]$

Thus, the required metal age for 12 yes old children is from 9.6 to 16.8.

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