Q42. If A and B together can compete a work in 18 days, A and C together in 12 days, and B and C together in 9 days, then B alone can do the work in

(a) 18 days

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(b) 24 days

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(d) 40 days

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Solution

The correct option is B
(b) 24 days

$(A + B)^{'} s o n e d a y w o r k = \frac{1}{18} (B + C)^{'} s o n e d a y w o r k = \frac{1}{9} (C + A)^{'} s o n e d a y w o r k = \frac{1}{12} 2 (A + B + C)^{'} s o n e d a y w o r k = \frac{2 + 4 + 3}{36} = - \frac{1}{4} (A + B + C)^{'} s o n e d a y w o r k = \frac{1}{8} B^{'} s o n e d a y w o r k = \frac{1}{8} - \frac{1}{12} = \frac{3 - 2}{24} = \frac{1}{24} B a l o n e c a n d o t h e w o r k i n 24 d a y s$

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Q42. If A and B together can compete a work in 18 days, A and C together in 12 days, and B and C together in 9 days, then B alone can do the work in

The correct option is B (b) 24 days (A+B)′s one day work =118(B+C)′s one day work =19(C+A)′s one day work =1122(A+B+C)′s one day work =2+4+336=−14(A+B+C)′s one day work =18B′s one day work =18−112=3−224=124B alone can do the work in 24 days