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- Three professors Dr. Gupta, Dr. Sharma, Dr. Singh are evaluating answer script of a subject. Dr. Gupta is 40% more efficient than Dr. Sharma, who is 20% more efficient than Dr. Singh. Dr.
Three professors Dr. Gupta, Dr. Sharma, Dr. Singh are evaluating answer script of a subject. Dr. Gupta is 40% more efficient than Dr. Sharma, who is 20% more efficient than Dr. Singh. Dr. Gupta takes 10 days less than Dr. Sharma to complete the evaluation work. Dr. Gupta starts the evaluation work and works for 10 days and then Dr. Sharma takes over. Dr. Sharma evaluates for next 15 days and then stops. In how many days, Dr. Singh can complete the remaining evaluation work?
7.2 days
9.5 days
11.5 days
None
Answers (1)
Let's solve this step by step
1)let's Dr.Singh's efficiency be x units/days
Then Dr.sharma = 20% more = 1.2x
Dr.Gupta = 40% more than Sharma = 1.4 x 1.2x = 1.68x units/days
2) Dr.Gupta takes 10 days less than Dr.Sharma
Time taken by sharma = S
Then Gupta's time = S- 10 days
Work = Efficiency x Time
So , 1.2x x S = 1.68x x(S-10)
Cancel x :
1.2S = 1.68( S - 10 )
1.2S = 1.68S - 16.8
0.48s = 16.8
S = 35
So , Dr.Sharma takes 35 days
Dr.Gupta takes 25 days
3) find total work : using Dr.Gupta's rate and time :
Work = 1.68x x 25 = 42x units
4) work done by gupta 10 days = 1.68x x 10 = 16.8x
work done by Sharma in 15 days = 1.2x x 15 = 18x
Total work done = 16.8x + 18x = 34.8x
Remaining= 42x - 34.8x = 7.2x
5) Dr.Singh's rate = x
Time = Work /Rate = 7.2x / x = 7.2 days
Answer : Option 1 ( 7.2 days )
