$T(9)= 1 +min(T(y),T(z)),$
Here, T(9) is nothing but min steps required to move from $9\rightarrow 100$.
For T(9) we have only 2 choices, i.e either we can take a shortcut to 15 or we can just move by 1 unit to right that is to10.
Let’s assume we didn’t took shortcut and we are simply moving 1 unit by right(i.e we reached to 10) and then, started moving right by 1 unit till 100, Bcz we only know shortcut for 9, for the rest of the numbers we don't know.
i.e $9\rightarrow 10\rightarrow 100$,
(100- 10= 90 +1= 91) steps are required, +1 bcz $9\rightarrow 10 $, 1 step is required.
okay, Now lets assume we took a shortcut from $9\rightarrow 15\rightarrow 100$,
Now min no.of steps required is (100-15 = 85 +1 =86 steps ) , +1 is for $9\rightarrow 15$. here also same as for the above reasoing i.e we dont know shortcut for 15 so we are moving right by simply 1 unit till 100. therefore it took 85 steps min.
By, the above complete reasoning we got to know that $min(T(y), T(z)),$ should be either 85 or 90(since, +1 is already given),
As we see,
T(10) is giving exactly 90 min steps(100-10=90), since we don't know the shortcut for 10, we move by 1 unit to right till 100,
and T(15) is giving exactly 85 min steps(100-15=85), since we don't know the shortcut for 15, we move by 1 unit to right till 100,
$T(9)= 1 +min(T(y),T(z)),$ = 1+ min(T(10), T(15)) = 1 +min (90,85) =1 + 85 = 86.
so,By Observing the above senario, y=10. z=15.
$\therefore$ Ans is 10*15 =150.