A few days ago I asked what the next pair of numbers in this series is:

49, 1
50, 10
53½, 21½
55, 25
60½, 35½
62, 38

has posted the correct answer:
70,50

The diference between the squares of each pair of numbers is 2400:
49² – 1² = 2401 – 1 = 2400 (48*50)
50² – 10² = 2500 – 100 = 2400 (40*60)
53½² – 21½² = 2862¼ – 462¼ = 2400 (32*75)
55² – 25² = 3025 – 625 = 2400 (30*80)
60½² – 35½² = 3660¼ – 1260¼ = 2400 (25*96)
62² – 38² = 3844 – 1444 = 2400 (24*100)
70² – 50² = 4900 – 2500 = 2400 (20*60120)

And so on up to 1200½² – 1199½² = 1441200¼ – 1438800¼ = 2400 (1*2400).