PSA_LEVEL-UP_QNR27. Two grain thrashers managed to thrash the gathered wheat in 4 days. If one of them thrashed half the wheat and subsequently the other thrashed the other half, they would complete the job in 9 days. How many days would it take for the faster grain thrasher to do the job if he works alone?
Let us take some numbers to understand the solution better.
Assume that there is 72 kg of grain to be thrashed. And this whole task is completed in 4 days when they work together. This means in one day amount of grain thrashed =
72/4 = 18 kg
Now, let us assume that to thrash half the amount of grain or 36 kg one person takes ‘x’ days and the other takes ‘9-x’ days. Thus, their one day work can also be equated as below
36/x + 36/(9-x) = 18
=>2/x + 2/(9-x) =1
=>2(9-x)+ 2x= x(9-x)
=> 18 – 2x + 2x = 9x -x²
Thus, one person takes 6 days and the other 3 days to finish half of the entire task working alone. To finish the entire task, the slower thrasher will take 12 days and the faster one 6 days. Option B.
If both the thrashers had equal efficiency each of them would finish the entire task in 8 days working alone. [2*4=8]. We understand from the question that one takes lesser time than the other; we can DEFINITELY say that the faster would take days lesser than 8 [and also greater than 4] and there is only one option satisfying that. Option B. This question does not essentially need any calculation!!!