I remember back to early 2005 (before going for my post graduation), when I’d just started preparing for some competitive examination, that even though I had great ambitions, my knowledge, expertise, and confidence as a student was sorely lacking. My love for internet (as a source of information) made me stumble through various places on the web to know maths short cuts and quick maths tricks, but without much to gain from it.
Now, after having being there and facing it all as a student first and then as a facilitator (though I take good number of Quants classes for CAT aspirants, I would not liked to be called a tutor or a teacher. These titles should be reserved for people of great wisdom and learning) for over 4-5 years I felt I had a really good grip on things; and even then, there were many things I am still struggling with
Let The Process Begin
I’m starting the process by posting below an interesting formula of the topic- time and work . The aim is to initiate the process of collaborative learning. So anyone who wants to make a difference can post a comment with any explanation, formula, shortcut, trick, solved examples, etc. on the same topic (Time and Work for this post). If you’ve any question related to any topic in maths you can post it on the question-answer platform on this site.
You can also help by sharing the information of this platform with your friends or anyone who wants to help others and learn from others in the process.
Time and Work Formula
I think the single most useful formula for the topic Time and Work is
N1H1D1E1W2 = N2H2D2E2W1
N1 and N2 = number of person
H1 and H2 = Hours worked by per person per day (assumed constant)
D1 and D2 = days
E1 and E2 = Efficiency
W1 and W2= Amount of work done
Consider this example to understand the applicability of this formula –
A piece of work can be done by 16 men in 8 days working 12 hours a day.How many men are needed to complete another work, which is three times the first one,in 24 days working 8 hours a day. The efficiency of the second group is half that of the first group?
N1H1D1E1W2 = N2H2D2E2W1
16*12*8*1*3 = N2*8*24*0.5*1
N2 = (16*12*8*1*3)/ (8*24*0.5*1) = 48
So number of men required is 48.
Note – you can remove anything from formula is not given in the question. For example if the question would have been –
“A piece of work can be done by 16 men in 8 days working 12 hours a day.How many men are needed to complete another work, which is three times the first one,in 24 days working 8 hours a day.”
The applicable formula would have been –
N1H1D1W2 = N2H2D2W1
Since nothing is mentioned about efficiency, we remove it from both sides.