3425 is to be divided among X, Y and Z in such a way that if X share reduced by 55, Y share reduced by Rs 40 and Z share increased by 45 then rest of the amount distributed among them in ratio 4:5:6. find the share of X.

Let original shares be X, Y, Z. After modifications: X-55, Y-40, Z+45 are distributed in ratio 4:5:6. Total after modifications = 3425-55-40+45 = 3375. If new amounts are 4k, 5k, 6k, then 15k = 3375, k = 225. So new amounts: 900, 1125, 1350. Original shares: X=900+55=955, Y=1125+40=1165, Z=1350-45=1305. Check: 955+1165+1305=3425. ✓