Question

A and B can do a piece of work in 12 days, B and
8 days, and C and A in 6 days. How long would
take to do the same work alone?
(a) 24 days (b) 32 days (c) 40 days
(d) 48 days (e) None of these
​

Answer 1

$\orange{ \sf{ \large{ \boxed{d)48 \: days}}}}$

$\sf{(A + B)’s \: 1 \: day’s \: work = \frac{1}{12} - - - - - - - - - - - - (1)}$

$\sf{(B + C)’s \: 1 \: day’s \: work = \frac{1}{8} - - - - - - - - - - - - (2)}$

$\sf{(C + A)’s \: 1 \: day’s \: work = \frac{1}{6} - - - - - - - - - - - - (3)}$

$\sf{ \blue{Adding \: eqution \: 1,\: 2,\: and \: 3}}$

$\sf{2(a + b + c) = }$

$\sf{ \frac{1}{12} + \frac{1}{8} + \frac{1}{6} = \frac{2 + 3 + 4}{24} = \frac{9}{24} }$

$\sf{hence \: (A + B + C)'s \: 1 \: day \: work = \frac{9}{24 \times 2} = \frac{9}{48} }$

$\sf{On \: subtracting \: (III) \: from \: (IV), \: B’s \: 1 \: day’s \: work \frac{9 }{48} - \frac{1}{6} }$

$\sf{B’s \: 1 \: day’s \: work  = \frac{9 - 8}{48} = \frac{1}{48} }$

$\sf{ \green{Hence ,\: B \: can \: completed \: the \: work \: in \: 48 \: days}}$

Hope this helps you mate ✌