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Question

A and B can do a piece of work in 72 days. B and C can do it in 120 days. A and C can do it in 90 days. In what time can A alone do it ?


A
120 days
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B
150 days
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C
180 days
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D
200 days
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Solution

The correct option is A 120 days
(A + B)'s 1 days' work = $$\displaystyle \cfrac{1}{72}$$; 
(B + C)'s 1 days work = $$\displaystyle \cfrac{1}{120}$$; 
(A + C)'s 1 days' work = $$\displaystyle \cfrac{1}{90}$$
$$\displaystyle \therefore (A+B)'s+(B+C)'s+(A+C)'s$$ 1 days work $$\displaystyle =\cfrac{1}{72}+\cfrac{1}{120}+\cfrac{1}{90}=\cfrac{5+3+4}{360}=\cfrac{12}{360}=\cfrac{1}{30}$$
$$\displaystyle \Rightarrow 2(A+B+C)'s$$ 1 days' work $$\displaystyle =\cfrac{1}{30}\Rightarrow (A+B+C)'s$$ $$\displaystyle =\cfrac{1}{60}$$
$$\displaystyle \therefore$$ A's 1 days' work = (A+B+C)'s 1 days' work - (B+C)'s 1 days' work 
$$\displaystyle =\cfrac{1}{60}-\cfrac{1}{120}=\cfrac{2-1}{120}=\cfrac{1}{120}$$
$$\displaystyle \therefore$$ A alone will complete the work in 120 days

Mathematics

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