A company has 3 category of Labours, Category A, B and C. 1 Labour of Category A, 3 of B and 4 of C can do a piece of work in 96 hrs, 2 of A and 8 of C can do it in 80 hrs, 2 of A and 3 of B can do it in 120 hrs, 5 of A and 12 of C can do it in
1). \(39\frac{1}{{11}}{\rm{hrs}}\)
2). \(42\frac{7}{{11}}\;{\rm{hrs}}\)
3). \(43\frac{7}{{11}}{\rm{\;hrs}}\)
4). 44 hrs
(2 A + 8 C)’s 1 hour work = 1/80
⇒ (1 A + 4C)’s 1 hour work = 1/160
? (1A + 3B + 4C)’s 1 hour work = 1/96
∴ 3B’s 1 hour work = (1/96) – (1/160) = 1/240
∴ (2A + 3B)’s 1 hour work = 1/20
∴ 2A’s 1 hour work = 1/120 – 1/240 = 1/240
? (2A + 8C)’s 1 hour work = 1/80
8C’s 1 hour work = 1/80 – 1/240 = 2/240 = 1/120
∴ (5A + 12C)’s 1 hour work = 5/(2 × 240) + 12/(8 × 120) = 1/96 + 1/80
= 176/(80 × 96) = 11/480
∴ (5A + 12C) will finish $(= \frac{{480}}{{11}}\; = \;43\frac{7}{{11}})$ hrs