## Slot -2 – Quantitative Aptitude – Arithmetic – Time and Work – Ramesh and Ganesh can together complete

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?

a) 14.5

b) 12

c) 11

d) 13.5

Solution:

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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## Slot -1 – Quantitative Aptitude – Arithmetic – Time and Work – When they work alone, B needs 25%

When they work alone, B needs 25% more time to ﬁnish a job than A does. They two ﬁnish the job in 13 days in the following manner: A works alone till half the job is done, then A and B work together for four days, and ﬁnally B works alone to complete the remaining 5% of the job. In how many days can B alone ﬁnish the entire job?

a) 22

b) 18

c) 20

d) 16

Solution:

ratio of time taken by A and B to complete the work alone = 1: 1.25 = 4x : 5x

As A complete half of the work alone  and B complete 5% of the work alone, so they will complete remaining 45% of work in 4 days .

So time taken by them to complete the whole work together = 4 * 100/45 = 80/9

Or (4x*5x)/(4x+5x) = 80/9

x = 4

Thus time taken by B to complete the work alone = 5x = 20 days

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## Slot -1 – Quantitative Aptitude – Arithmetic – Time and Work – Humans and robots can both perform

Humans and robots can both perform a job but at diﬀerent eﬃciencies. Fifteen humans and ﬁve robots working together take thirty days to ﬁnish the job, whereas ﬁve humans and ﬁfteen robots working together take sixty days to ﬁnish it. How many days will ﬁfteen humans working together (without any robot) take to ﬁnish it?

a) 36
b) 40
c) 45
d) 32

Solution:

Given, 15/H+5/R=1/30  ——-1)
And 5/H+15/R=1/60  ——–2)

By solving eq 1) & eq 2) we get
1/(H )=1/(40×12)

Thus H = 40×12
So time taken by 15 humans = 40×12/15=32

## Online Coaching Course for CAT Exam Preparation

a) 750+ Videos covering entire CAT syllabus
b) 2 Live Classes (online) every week for doubt clarification
c) Study Material & PDFs for practice and understanding
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