A garden is 24 m long and 14 m wide. There is a path 1 m wide outside the garden along its sides. If the path is to be constructed with square marble tiles 20 cm × 20 cm, the number of tiles required to cover the path is

Step 1: Convert all dimensions to centimetres.
Garden length:
$24~m = 24 \times 100 = 2400~\mathrm{cm}$
Garden width:
$14~m = 14 \times 100 = 1400~\mathrm{cm}$
Path width:
$1~m = 1 \times 100 = 100~\mathrm{cm}$
Tile side length:
$20~\mathrm{cm}$

Step 2: Calculate total dimensions of garden plus path.
Total length:
$2400~cm + 2 \times 100~cm = 2600~\mathrm{cm}$
Total width:
$1400~cm + 2 \times 100~cm = 1600~\mathrm{cm}$

Step 3: Calculate area of total region.
$2600~cm \times 1600~\mathrm{cm}$
First, $2600 \times 1000 = 2\,600\,000~cm^2$
Then, $2600 \times 600 = 1\,560\,000~cm^2$
Total area:
$2\,600\,000~cm^2 + 1\,560\,000~cm^2 = 4\,160\,000~cm^2$

Step 4: Calculate garden area.
$2400~cm \times 1400~\mathrm{cm}$
First, $2400 \times 1000 = 2\,400\,000~cm^2$
Then, $2400 \times 400 = 960\,000~cm^2$
Garden area:
$2\,400\,000~cm^2 + 960\,000~cm^2 = 3\,360\,000~cm^2$

Step 5: Calculate path area.
$4\,160\,000~cm^2 - 3\,360\,000~cm^2 = 800\,000~cm^2$

Step 6: Calculate area of one tile.
$20~cm \times 20~cm = 400~cm^2$

Step 7: Calculate number of tiles required.
$\frac{800\,000~cm^2}{400~cm^2}$
$800\,000 \div 400 = 2000$
The number of tiles required is $\boxed{2000}$.