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Quantitative Reasoning – Practice – Time and Work – Find out if you could solve without solving!!!

time and work shortcut

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?
A) 12
B) 6
C) 15
D) 18

Ans:

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
=> x²-9x+18=0
=> x=6,3

(9-x)=3,6

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.

Shortcut
———
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!!!

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