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Ramesh and Ganesh can together complete | Quantitative Aptitude - Arithmetic – Time and Work

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The question below is from previous year CAT question from CAT 2018 exam comes from  CAT Time and Work: Ramesh and Ganesh can together complete. Find out by answering this question which tests an aspirant’s Quantitative Ability Skills:

CAT 2018 - Slot-2 - Arithmetic - Question-1 - Ramesh and Ganesh can together complete

Q. 1: Ramesh and Ganesh can together complete a work in 16 days. After seven days of working together, Ramesh got sick and his efficiency fell by 30%. As a result, they completed the work in 17 days instead of 16 days. If Ganesh had worked alone after Ramesh got sick, in how many days would he have completed the remaining work?
1. 13.5
2. 11
3. 12
4. 14.5

Let Ram do x unit of work each day, working with his full efficiency.

So work done by him in last ten days ( when his efficiency dropped by 30% ) = 0.7 *10x = 7x

Had he worked with his full efficiency he must have done 9x unit work in last 9 days , thus Ganesh must have done (9x -7x = 2x) work on 17th day.

Thus ratio of efficiency of Ram and Ganesh = 1:2

So total work = 16×(x+2x)=48x

Work remaining after 7 days = 48x-7×3x=27x

Time taken by Ganesh to complete this work = 27x/2x=13.5

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