Question
Download Solution PDFA & B together do a work in 12 days. B & C together do in 15 days, C & A together do in 20 days. If all work together then in how many days the 2/5th part of work will complete.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A + B = 12 days
B + C = 15 days
C + A = 20 days
Formula used:
Time = Work ÷ Efficiency
Calculation:
LCM of 12, 15, 20 = 60 units (Total Work)
(A + B)'s efficiency = 60 ÷ 12 = 5 units/day
(B + C)'s efficiency = 60 ÷ 15 = 4 units/day
(C + A)'s efficiency = 60 ÷ 20 = 3 units/day
Add all: (A + B) + (B + C) + (C + A) = 5 + 4 + 3 = 12 units/day
⇒ 2A + 2B + 2C = 12 units/day
⇒ A + B + C = 6 units/day
2/5 of total work = 2/5 × 60 = 24 units
Time = 24 ÷ 6 = 4 days
∴ 2/5th of work will complete in 4 days.
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