Question

if A and B together can complete work in 18 days, A and C together in 12 days and B and C together in 9 days, then b alone can do work in how much day.
a_ 18 days
b_ 24days
c_ 30 days
d_ 40 days​

Answer 1

Step-by-step explanation:

24 days

(A + B)’s 1 day’s work = \frac{1}{18}

(B + C)’s 1 day’s work = \frac{1}{9}

(C + A)’s 1 day’s work = \frac{1}{12}

On adding all above equations, we get

2 (A +B + C)’s 1 day’s work = \frac{1}{18} + \frac{1}{9} + \frac{1}{12} = \frac{2+4+3}{36} = \frac{9}{36} = \frac{1}{4}

∴ (A + B + C)’s 1 day’s work = \frac{1}{8}

Now, B’s 1 day’s work = (A + B + C)’s 1 day’s work – (A + C)’s 1 day’s work

= \frac{1}{8}-\frac{1}{12}=\frac{3-2}{24}=\frac{1}{24}

Hence B alone can do the work in 24 days. So option [B] is correct answer.