CAT Exam Model Paper 4 with solutions for free online practice

Question : 22 of 60

Marks: +1, -0

When working alone A, B and C can complete a piece of work in 8, 12 and 30 days respectively. At the most only two people can work on each day and nobody works for more than two consecutive days. What is the minimum number of days that they will take to finish the work?

4 $4 /29$
6 $4/25$
6 $6/29$
12 $4/25$

Validate

Solution:

The maximum total work done for three consecutive days will be when A, B and C work in distinct pairs (for example ‘A and B’, ‘B and C’ and 'C and A’).
Hence on these three days fraction of total work done will be:

2 ( { 1 }/ { 8 } + { 1 } /{ 12 } + { 1 }/ { 30 } ) - { 58 }/ { 120 }

Maximum possible work done in the first 6 days

2 ( { 1 }/{ 8 } + { 1 } /{ 12 } + { 1 } /{ 30 } ) = 2 ( { 58 } /{ 120 } ) = { 116 } /{ 120 }

The remaining

4/120

fraction of work can be done in least amount of time if A and B work together on the 7th day.
A and B together can do

{ 1 }/ { 8 } + { 1 } /{ 12 } = { 5 }/ { 24 }

fraction ofwork in a day.
So, they will complete the

4/120

fraction of work

{ 4 }/ { 120 } + { 5 } /{ 24 } = { 4 }/ { 25 } { \day }

Answer (in days) =

6 + { 4 } /{ 25 } = 6 { 4 }/ { 25 }

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