Problems based on Numbers Test 5

Let the three-digit number be 100x + 10y + z, then
x + y + z = 10 ...(i)
x + z = y ...(ii)
From equations (i) & (ii) we get, y = 5 and x + z = 5 ...(iii)
Again, 100z + 10y + x – (100x + 10y + z) = 99
⇒ 99z – 99x = 99
⇒ z – x = 1 ...(iv)
Solving (iii) and (iv), we get x = 2, z = 3.
Hence, number = 100 × 2 + 10 × 5 + 3 = 253