Question

A and B can do a piece of work in 12
days, B and C in 8 days, and C and A
in 6 days. How long would B take to do
the same work alone?
(1) 24 days
(2) 32 days
(3) 40 days
(4) 48 days
(5) None of these​

Answer 1

Answer:

48 Days

Step-by-step explanation:

(A + B)’s 1 day’s work = 1/12……….(I)

(B + C)’s 1 day’s work = 1/8…….….(II)

(C + A)’s 1 day’s work = 1/6……….(III)

On adding,

2(A + B + C)’s 1 day’s work = 2(1/12+1/8+1/6)= 2+4+3/24=9/24

∴ (A + B + C)’s 1 day’s work = 9/24*2=9/48……….(IV)

On subtracting (III) from (IV),

B’s 1 day’s work = 9/48-1/6

= 54-48/288=6/288=1/48

∴ B can complete the work in 48 days.

Hence option [D] is correct answer