Question

Match the problems from List I, where you have to find the ages of both, to the solutions provided in List II:

Answer 1

(A) Let the smaller number be $x$.
Then, $18x+x^2=208$
$x^2+18x-208=0$
$x^2+26x-8x-208=0$
$x(x+26)-8(x+26)=0$
$x=8,-26$
$\therefore {\text{(larger number)}}^2=18\left(8\right)=144$
$\text{larger number}=12$

(B) Let the son's present age be $x$.
Then, father's age = $x^2$
Now, $x^2-1=8(x-1)$
$x^2-8x+7=0$
$x^2-7x-x+7=0$
$(x-7)(x-1)=0$
$x=1,7$
$\therefore$ Father's age = $(7{)}^2=49$

(C) Let the son's age be $x$.
Father's age = $x^2$
$x^2+5x=66$
$x^2+5x-66=0$
$x^2+11x-6x-66=0$
$x(x+11)-6(x+1l)=0$
$x=6,11$
$\therefore$ Father's age = $(6{)}^2=36$

(D) Let the John's present age be $x$.

$2$ years ago, Jacob's age was three times the square of John's age

i.e., Jacob's present age is $3(x-2{)}^2+2$

In three years' time, John's age will be one-fourth of Jacob's age

i.e., $(x+3)=\frac{3(x-2{)}^2+2+3}{4}$

$\Rightarrow 4x+12=3x^2+17-12x$

$\Rightarrow 3x^2-16x+5=0$

$\Rightarrow (x-5)(3x-1)=0$

$\Rightarrow x=5$ or $x=\frac{1}{3}$

$\therefore$ John's age $=5$ and Jacob's age $=29$