Three Professors Dr. Gupta, Dr. Sharma and Dr. Singh are evaluating answer scripts 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 man days, Dr. Singh can complete the remaining evaluation work.

let G be number of days in which Dr. gupta can complete the evaluation of answer sheet , let Sh be number of days in which Dr. Sharma can complete the evaluation of answer sheet , let Si be number of days in which Dr. Singh can complete the evaluation of answer sheet

Given Dr. Gupta is 40% more efficient than Dr. Sharma therefore number of days required by Dr. Sharma to complete the evaluation of answer sheet = 1.4*G

Dr. Gupta takes 10 days less than Dr. Sharma to complete the evaluation work i.e. 1.4G-G = 10 therefore G = 25 and hence Sh = 35

Also given that Dr. Sharma is 20% more efficient than Dr. Singh therefore number of days required by Dr. Singh to complete the evaluation of answer sheet = $$\frac{35}{1.2}$$ = 42 i.e. Si = 42

Dr. Gupta starts the evaluation work and works for 10 days therefore he completes $$\frac{10}{25}$$ of work then Dr. Sharma takes over. Dr. Sharma evaluates for next 15 days therefore he completes $$\frac{15}{35}$$ of work. Fraction of work left is 1 - $$\frac{10}{25}$$ - $$\frac{15}{35}$$ = $$\frac{6}{35}$$ now time required by Dr. Singh to complete this amount of work is $$\frac{6*42}{35}$$ = 7.2 days

Therefore our answer is option 'A'