Question

Ram can complete the work in 10 hours, Ajit in 12 hours and Suresh in 15 hours. All of them began the work together, but Ram had to leave the work after 2 hours of the start and Ajit left 3 hours before the completion of the work. How long did the work last? Select one:
a. 7 hrs
b. 8 hrs
c. 9 hrs
d. Cannot be determined

Answer 1

D. Because Ram only did 2 hours so then that makes 2 hours of work done but then left for whatever reason. Ajit left 3 hours BEFORE the completion of the work and that gives us info that there were hours put in between both Rams and Ajits work. They all started at the same time so it doesn't mean that Ajit didn't do any of the work. Ajit can work for 12 hours POSSIBLY. It did not say he can exact. So it leaves to Suresh that can work up to 15 hours of the work but we dont know how long he did it. Suresh either could just gone over or less than 15 hours. 

If this answer was way out of the question then i am sorry and i probably was wrong. 

Answer 2

Answer:

Option A is the correct answer.

Step-by-step explanation:

Let the work be W.

Ram can complete the work in 10 hours, Ajit in 12 hours and Suresh in 15 hours.

$\texttt{Rate of Ram =}\frac{W}{10}\\\\\texttt{Rate of Ajit =}\frac{W}{12}\\\\\texttt{Rate of Suresh =}\frac{W}{15}$

Ram had to leave the work after 2 hours of the start and Ajit left 3 hours before the completion of the work.

Let t be the time of work completion,

We have

              $W=2\times \frac{W}{10}+(t-3)\times \frac{W}{12}+t\times \frac{W}{15}\\\\1=\frac{1}{5}+\frac{t-3}{12}+\frac{t}{15}\\\\12+5(t-3)+4t=60\\\\9t=63\\\\t=7hours$

Option A is the correct answer.