Question

Three professors from Harvard University Dr. Tarun Khanna, Dr. James G Anderson and Dr. David
Clarke jointly take a course on Behavioural Science. At the end of the course they conduct and
exam and grade students based on their answer scripts.
Dr. Khanna is 40% more efficient than Dr. Anderson, who is 20% more efficient than Clarke. Dr.
Khanna takes 10 days less than Dr. Anderson to complete the student grading.
Dr. Khanna starts the evaluation work and works for 10 days and then Dr. Anderson takes over. Dr.
Anderson evaluates for next 15 days and then stops. In how many days, Dr. Clarke can complete
the remaining student answer evaluation ?
9.5 Days
12 Days
7.2 Days
13.5 Days​

Answer 1

Given : Dr. Khanna is 40% more efficient than Dr. Anderson, who is 20% more efficient than Clarke. Dr.

Khanna takes 10 days less than Dr. Anderson to complete the student grading.

Dr. Khanna starts the evaluation work and works for 10 days and then Dr. Anderson takes over. Dr.

Anderson evaluates for next 15 days and then stops

To Find :  In how many days, Dr. Clarke can complete the remaining student answer evaluation  

9.5 Days

12 Days

7.2 Days

13.5 Days​

Solution:

Dr. Khanna is 40% more efficient than Dr. Anderson,

Dr. Anderson is 20% more efficient than Clarke

Let say Dr. Clarke  1 day work  = x

then  Dr. Anderson 1 day work = x + (20/100)x  = 1.2x

Dr. Khanna 1 day work  =  1.2x + (40/100)1.2x  = 1.68x

Dr. Khanna takes 10 days less than Dr. Anderson

=> D ( 1.2x)  = (D  - 10)1.68x

=> 1.2D = 1.68D  - 16.8

=> 0.48D = 16.8

=> D = 35

Hence Dr. Anderson  takes 35 days to complete the work

and Dr Khanna takes  25 days to work

and work is  =  35 * 1.2x = 25 * 1.68x  =  42x

Hence  Dr. Clarke take 42 day to complete the work

Dr. Khanna  works for 10 days = 10 * 1.68x  = 16.8x

Dr. Anderson evaluates for next 15 days  = 15 * 1.2x  = 18x

Work remaining = 42x - 16.8x - 18x

= 7.2x

Days taken by Dr. Clarke     = 7.2x/x  = 7.2 Days

Dr. Clarke can complete the remaining student answer evaluation in 7.2 Days

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