Question

One's intelligence quotient or IQ varies directly as a person's mental age and inversely as that person's chronological age. A person with a mental age of 15 and a chronological age of 25 has an IQ of 120. What is the chronological age of a person with a mental age of 20 and an IQ of 100? The chronological age is what?

Answer 1

Given that,

IQ varies directly as a person's mental age

$\inline I.Q\alpha MentalAge$

IQ varies inversely as that person's chronological age.

$\inline I.Q\alpha \frac{1}{ChronologicalAge}$

Combining both

$\inline I.Q\alpha \frac{MentalAge}{ChronologicalAge}$

Equating to a constant k

$\inline I.Q=k \frac{MentalAge}{ChronologicalAge}$

Given that a person with a mental age of 15 and a chronological age of 25 has an IQ of 120

$\inline 120=k \frac{15}{25}$

$\inline k=120\times \frac{25}{15}$

Given another mental age of 20 and an IQ of 100

$\inline I.Q=k \frac{MentalAge}{ChronologicalAge}$

$\inline 100=k\frac{20}{ChronologicalAge}$

Put $\inline k=120\times \frac{25}{15}$

$\inline 100=120\times \frac{25}{15}\times\frac{20}{ChronologicalAge}$

$\inline 100=120\times \frac{5}{3}\times\frac{20}{ChronologicalAge}$

$\inline 100=40\times \frac{5}{1}\times\frac{20}{ChronologicalAge}$

$\inline ChronologicalAge=40\times \frac{5}{1}\times\frac{20}{100}$

$\inline ChronologicalAge=4\times \frac{5}{1}\times\frac{2}{1}$

$\inline ChronologicalAge=40$

Therefore,

Chronological age of a person with a mental age of 20 and an IQ of 100 is 40