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?

60 days
90 days
115 days
120 days

Correct Answer: 120 days

Explanation:

Combined efficiency of A and B = 1/72 ....(i)
Combined efficiency of B and C = 1/120 ....(ii)
Combined efficiency of A and C = 1/90 ....(iii)
On adding Eqs. (i), (ii) and (iii), we get
2(A + B + C) = 1/72 + 1/120 + 1/90 = (5 + 3 + 4)/360
= 12 / 360 = 1 / 30
⇒ A + B + C = 1/60 .....(iv)
i.e Combined efficiency is 1/60 or we can say together A, B and C can complete the work in 60 days.
On subtracting Eq. (ii)from Eq. (iv), we get
Efficiency of A = Combined efficiency of A, B and C - Combined efficiency of B and C
= 1/60 - 1/120 = 1/120
Hence, A alone can do it in 120 days

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