If (a – 7) (b – 10) (c – 12) = 1000, the least possible value of (a + b + c) is

The values of a, b, c will be minimum if

(a – 7) = (b – 10) = (c – 12)

⇒ (a – 7) (b – 10) (c – 12)

= 10 × 10 × 10

∴ a – 7 = 10 Ÿ a = 17

b – 10 = 10 Ÿ b = 20

c – 12 = 10 Ÿ c = 22

∴ a + b + c = 17 + 20 + 22 = 59