# Difficult Time and Work Solved QuestionAptitude Discussion

 Q. 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?
 ✔ A. 7.2 days ✖ B. 9.5 days ✖ C. 11.5 days ✖ D. None of these

Solution:
Option(A) is correct

As per the information given, the ratio of efficiencies of Dr. Gupta, Dr. Sharma and Dr. Singh are $42:30:25$

Hence, the ratio of time taken by Dr. Gupta and Dr. Sharma = $5:7$

Dr. Gupta takes 10 days less than Dr. Sharma, time taken by them will be 25 days and 35 days respectively.

Hence, time taken by Dr. Singh will be 42 days.<br>Part of work completed by Dr. Gupta$=\dfrac{2}{5}$

Part of work completed by Dr. Sharma$=\dfrac{2}{7}$

Remaining work

$=1-\left(\dfrac{2}{5}+\dfrac{3}{7}\right)$

$=\dfrac{6}{35}$

will be completed by Dr. Singh

He can complete it in

$42\times \dfrac{6}{35}=7.2$days