Mr Raja paid a total of $1406.40 for a laptop and a camera at a sale. The price of the camera before discount was $864. What was the price of the laptop before discount?

1. Determine which item is the 1st item and which is the 2nd item by testing the case where the camera is the 2nd item.

Assume the camera is the 2nd item (20% discount). Its discounted price would be $864 \times (1 - 0.20) = 864 \times 0.8 = \char36{}691.20$.
The discounted price of the laptop would then be $1406.40 - 691.20 = \char36{}715.20$.
Since the laptop is the 1st item (10% discount), its original price would be $715.20 \div 0.9 = \char36{}794.67$.
Check condition: Price of 2nd item (camera, $864) must be$\le$1st item (laptop,$794.67). This is false ($864 > 794.67$).
Therefore, the camera must be the 1st item and the laptop must be the 2nd item.

2. Calculate the discounted price of the camera (1st item).

Since the camera is the 1st item, it gets a 10% discount.
Discounted price of camera = $864 \times (1 - 0.10) = 864 \times 0.9 = \char36{}777.60$.

3. Calculate the discounted price of the laptop.

Discounted price of laptop = Total paid - Discounted price of camera
$= 1406.40 - 777.60 = \char36{}628.80$.

4. Calculate the original price of the laptop (2nd item).

The laptop is the 2nd item, so it gets a 20% discount.
Original price of laptop = $628.80 \div (1 - 0.20) = 628.80 \div 0.8 = \char36{}780$.
(Check condition: Price of 2nd item ($780)$\le$1st item ($864). This is true.)