Aptitude - Time and Work - Discussion

Please explain how come 5/48?

All the explanations are really amazing and understandable. But I would like to add a point to the discussion. Why did we do 1/16, 1/12 or 1/4. See there is lot frequency distribution in the values. So to ease our lives we want to compare all this to a benchmark value.

In this case everybody is taking different number of duration's to complete a particular task. So first we want to find out how much work everybody was able to complete in any particular day. Just to make the calculations easier.

And if one can do (1/16)th part of a work in one day, then just by reversing the fraction we can get to know in total how many days he/she will be able to complete the entire task.

Hope this will help.

How do you get 1/4?

Answer of C work 5/48 to 48/5.

This is one day work of C.

Example as given in question itself.

A work complete in 16 day so in 1 day 'a' will complete 1/16 portion of whole work. Whole work completed by a is 16/1=16 days.

Tell me any one that c's work. I can't understand it.

Easiest method.

LCM is 48 of 16 &12. Then A can complete work in 3 work and B can 4 work.

Now A B C can complete 12 work.

Now A and B complete 7 work so still remaining work is 5.

So C can alone complete work 48/5. So answer is C. You can easily calculate.

Where does 48 come from in this come equation?

A can do work in 16 days.

Then, A's 1 day work = 1/16.

Meanwhile, C's 1 day work = 5/48 (our ans).

Then, C can do work in 48/5 days.

How to change this 5/48 to 48/5?

@Deepika.

C's 1 day work is 5/48.
Here we require C's total work.

Total work should be taken as '1'.

So, 1 day work i.e,5/48*number of days used to complete the work(unknown, so take it as 'x') = total work 1.

Simply, 5/48*x = 1.
5x = 48.
x = 48/5.

So C's total work is 48/5.