Gautam and Suhani, working together, can finish a job in 20 days. If Gautam does only 60% of his usual work on a day, Suhani must do 150% of her usual work on that day to exactly make up for it. Then, the number of days required by the faster worker to complete the job working alone is

The correct answer is 36.

Let the daily work rates (amount of work done per day) of Gautam and Suhani be represented by $G$ and $S$, respectively. Let the total work to be completed be $W$.

According to the problem, Gautam and Suhani working together can finish the job in 20 days. Therefore, the total work $W$ is given by:
$W=20(G+S)$

We are given that if Gautam does only 60% of his usual work on a day (which is $0.6G$), Suhani must do 150% of her usual work on that day (which is $1.5S$) to exactly make up for the deficit. This means the sum of their modified work rates on that day equals their usual combined work rate:
$0.6G+1.5S=G+S$

We can solve this equation to find the relationship between Gautam's and Suhani's work rates:
$1.5S-S=G-0.6G$
$0.5S=0.4G$
Multiplying both sides by 10:
$5S=4G$
$S=\frac{4}{5}G$

From the relation $S=0.8G$, we see that $G>S$, which means Gautam is the faster worker.

Now, we can express the total work $W$ purely in terms of Gautam's work rate $G$:
$W=20(G+\frac{4}{5}G)$
$W=20\left(\frac{9}{5}G\right)$
$W=4\times 9G$
$W=36G$

The number of days required by the faster worker (Gautam) to complete the job working alone is:
$\text{Days}=\frac{W}{G}=\frac{36G}{G}=36$

Thus, the faster worker will take 36 days to complete the job alone.