Laptops were sold at the discount stated below. Jian Hao paid a total of $5805 for 3 similar laptops during the 2023 Great SG Laptop Sales. The amount that he paid includes an 8% GST.

1. Calculate the total discounted price of the 3 laptops before GST.

Let the total discounted price be $D$.
Since the total paid includes an $8\%$ GST:
$108\% \text{ of } D = \char36{}5805$
$D = \frac{5805}{1.08} = \char36{}5375$

2. Express the total discounted price in terms of the original price of one laptop.

Let the original price of one laptop be $P$.
The discounts are $15\%$, $30\%$, and $40\%$.
Discounted price of 1st laptop = $(100\% - 15\%)P = 0.85P$
Discounted price of 2nd laptop = $(100\% - 30\%)P = 0.70P$
Discounted price of 3rd laptop = $(100\% - 40\%)P = 0.60P$
Total discounted price = $0.85P + 0.70P + 0.60P = 2.15P$

3. Solve for the original price of one laptop.

$2.15P = 5375$
$P = \frac{5375}{2.15} = 2500$
The original price of a laptop without GST is $\char36{}2500$.