The number of days required by A, B and C to work individually is 6, 12 and 8 respectively. They started a work doing it alternatively. If A has started then followed by B and so on, how many days are needed to complete the whole work?
A
8
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B
7.5
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C
8.5
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D
912
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Solution
The correct option is A 8
In 3 days A, B, C do 38 work in 6 days A, B, C do 34 work Rest work = 14 which is less than 38 On the 7th day, 16 more work will be done by A Now rest work 14−16=112 Now, this rest work (112) will be done by B in 1 complete day. Thus, total number of days = 6 + 1+ 1= 8 days
Alternate Method: Efficiency of A = 16.66% Efficiency of B = 8.33% Efficiency of C = 12.5% Efficiency of A + B = 25% Efficiency of A + B+C = 37.5% In 3 days A, B, C completes 37.5% work In 6 days A, B, C completes 75% work This 25% work will be completed by A and B in next 2 days Thus total 6 + 2 = 8 days are needed