To solve this expression, we need to follow the order of operations (PEMDAS).

First, let's convert the mixed numbers to improper fractions:

9/16 ÷ 3375 + 1 1/25 × 1 2/3 - 1/35 × 24.5
= 9/16 ÷ 3375 + 51/25 × 5/3 - 1/35 × 49/2
= 9/16 ÷ 3375 + 255/75 - 49/70

Next, perform the division:

9/16 ÷ 3375 = 9/16 ÷ 3375/1 = 9/16 × 1/3375 = 9/54000 = 1/6000

Now, substitute the division result back into the expression:

1/6000 + 255/75 - 49/70

Next, calculate the multiplication:

255/75 × 5/3 = 1275/225 = 51/9 = 17/3

Now substitute back into the expression:

1/6000 + 17/3 - 49/70

Lastly, calculate the final result:

1/6000 + 17/3 - 49/70 = 1/6000 + 3400/6000 - 294/6000 = 3401/6000 - 294/6000 = 3107/6000

Therefore, the final result is 3107/6000.