# Time and work important question #2-shortcut trick

Last time we have discussed a time and work most important question in which A left after P days. But this time we are discussing the different aspect of this type of question in which B joined after P days.

Suppose you are given a question like the one given below…

Q:- In a project work, A and B can do the work in 20 days and 12 days respectively. A started the work alone and after 4 days, B
joined him and they both completed the remaining work. In how many days the work was done?

Now this type of question is basically done by most of us first calculating the work done by A in 4 days. Then we subtracts  the work from whole work i.e. 1. And then we calculate how much time will A and B take to get the remaining work done when both of them does the work together. Then we get the amount of days both will take to complete the remaining work and then we have to add that time into the time that was given in the question i.e. 4 days. Then we get the total time in which the work will be completed.

Basic solution of the above problem is below----the shortcut trick is given below the basic solution. This is just to show the difference between both of the tricks

A can do the work in 20 days
So Work done by A in 1 day= 1/20
So work done by A in 4 days= 4/20 = 1/5
So the remaining work= 1-(1/5) =(5-1)/5 = 4/5
The remaining work was done by A and B together

Now
B can do the work in 12 days
So work done by B in 1 day= 1/12
Work done by both A and B together in 1 day= (1/20)+(1/12)= 32/240 work
So
32/240 work is done by both in = 1 day
So 4/5 work will be done by them in= [1*(4/5)]/(32/240)
=(240*4)/(32*5) = 6 days
So the remaining work was done by them in 6 days.
So total time taken in doing the whole work will be = 6+4 = 10 days

The above solution is the basic method that most of us uses to solve this type of questions.

But wait
This trick takes time of about 3-5 minute to solve or if you are faster, then still you will take nearly 30-60 seconds to solve this question to solve this question.
But here is the trick that will you solve this types of question in just 5-10 seconds with the derived formula trick.

This derived formula trick is for any question of this type but you should take care while reading the questions what is asked.
So here is the derived formula shortcut trick for this type of question: By A K Panchal
formula:
x[(P+y)/(x+y)]
P=4
x=20
y=12
putting the derived formula into the question
x[(P+y)/(x+y)]
=20[(4+12)/(20+12)]
=20[16/32]

= 10 days

So the work will be done in total of 10 days. So this shortcut derived formula takes just 8 seconds to solve.