Aptitude - Time and Work - Discussion

@Sunshine.

In the question, it was mentioned that B and C can finish the work in 12 days not only A.
then how you can said B's work = 12 days?

Please explain the step.

A can do the work = 16 days,
B can do the work =12days,
A+B+C together can do work =4 days.

let's take the LCM of 16,12 and 4 it is 48.
calculate the 1 day's work of A,B and A+B+C,
1day's work of A= 48/16= 3,
1day's work of B= 48/12= 4,
1day's work of A+B+C =48/4=12,
Here we calculate the 1day's work of c,
A+B+C=12,
3+4+C=12,
7+C=12,
C=12-7,
C=5.

Then,
c alone can do the work in;
C = 48/5 = 9 * 3/5 days.

common multiple for 12 and 16 is 48.

A's one day work =48/16=3 units,
B's one day work=48/12=4 units,
C's one day work??

A and B together do a piece of work in 4 days= 28 units.
remaining work ( C's work in 4 days)=48 - 20 =20 units,
C's work in one day=20/4=5 unit,
C alone can do the job in=(5 * 9)+3/5 = 9 3/5.

A = 16.
B = 12.

Lcm for 16,12 is 48.
16*3 = 48.
12*4 = 48.

With the help of c they did the job in 4 days only,
So 48/4=12.
12-(a+b).
12-(3+4) = 5
Now 48/5 = 9.6 hrs.

How come 5/48? Please explain.

A can do job in 16 days.
B can do in 12 days.

Make the LCM for both A and B.
After LCM we get 48.
This is the total work for both A and B=48.
For one day work of A is 16*3=48.

That means A can do 3 units of work per day,
For one day work of B is 12*4=48.

That means B can do 4 units of work per day.
(A+C)=3+4=7.
(B+C)=4+4=8.

TOTAL work of (A+B)and(B+C) = 7 + 8 = 15.

We find out c alone can do the job in how many days
So we can subtract 48-15=33.

Convert 33 in fraction form that you get the answer.

1/4- (1/16+1/12) = (1/4-7/48) please anyone explain this.

@Sai Kumar.

It is 1÷16 + 1÷12 so 1st do LCM of 16,12 then you'll get the answer as 48 later on divide (48÷16, 48÷12) then you'll get answers as 3 and 4 (as multiplied by the numerator 1 then 3*1 will be 3 and 4*1 will be 4) add 3+4 you'll get 7 then the final answer will be 7/48

Why 5/48 is 48/5 because A can do work in 16 days so his efficiency for 1 day is 1/16.

(which means (work/time)). So same for C's 1-day work is 5/48 and he can complete the work in 48/5.

@Bhimesh.

Yes, you are correct.