A’s one day’s work = 1/10
B’s one day’s work = 1/12
C’s one day’s work = 1/15
A, B and C’s one day’s work = 1/10 + 1/12 + 1/15
= (6 + 5 + 4)/60 = 15/60 = ¼
Let the work completed in x days
∴ A’s 2 days work + B’s (x – 3) days work + C’s x days work = 1
⇒ 2 × (1/10) + (x – 3) × 1/12 + x × (1/15) = 1
⇒ 1/5 + (x -3)/12 + x/15 = 1
(12 + 5x – 15 + 4x = 60)/60
(L.C.M of 5, 12, 15 = 60)
⇒ 9x = 60 – 12 + 15 ⇒ 9x = 63
⇒ x = 63/9 = 7
∴ Work will last for 7 days