Answer
$50 $.
Work Step by Step
Step 1:- Translate the statement to form an equation.
Let the IQ be $I$,
the mental age be $M$,
and the chronological age be $C$.
Because $I$ varies directly as $M$ and inversely as $C$, we have:
$\Rightarrow I=\frac{kM}{C}$ ...... (1)
Step 2:- Substitute the first set of values into the equation to find the value of $k$.
The given values are $M=25,C=20$
and $I=125$.
Substitute into the equation (1).
$\Rightarrow 125=\frac{k(25)}{20}$
Multiply both sides by $\frac{20}{25}$.
$\Rightarrow \frac{20}{25}\cdot 125=\frac{20}{25}\cdot \frac{k(25)}{20}$
Simplify.
$\Rightarrow 100=k$
Step 3:- Substitute the value of $k$ into the original equation.
Substitute $k=100$ into the equation (1).
$\Rightarrow I=\frac{100M}{C}$ ...... (2)
Step 4:- Solve the equation to find the required value.
Substitute $M=40$ and $I=80$ into the equation (2).
$\Rightarrow 80=\frac{100(40)}{C}$
Simplify.
$\Rightarrow 80=\frac{4000}{C}$
Multiply both sides by $\frac{C}{80}$.
$\Rightarrow \frac{C}{80}\cdot 80=\frac{C}{80}\cdot \frac{4000}{C}$
Simplify.
$\Rightarrow C=50$
Hence, the chronological age is $50 $.
