Aptitude - Time and Work - Discussion

Given that;
A complete the work in --> 16 days.
B complete the work in --> 12 days.
With the help of C (A+B+C) complete the work in --> 4 days.
We take LCM OF (16,12,4) comes --> 48 unit.
A complete --> 48/16 = 3 unit per day.
B complete --> 48/12 = 4 unit per day.
A+B+C complete --> 48/4 = 12 unit per day.
C alone do --> 12-3-4 = 5 unit per day.
so C take time to complete the work in days = total unit/unit per day by c.
= 48/5.
= 9(3/5) days.
When we divided 48 by 5 quotient comes to 9 and the remainder is 3 . it is a mixed fraction.

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.

@RaviKumar.

We have A+C = 4 -->A+C 1 day work = 1/4.

B+C = 4 --> B+C 1 day work = 1/4.

We add (A+C)+(B+C) = (1/4)+(1/4).

A+B+2C = (4+4)/(4*4) = 8/16 = 1/2.
A+B+2C = 1/2.
A+B+C = 1/(2*2) = 1/4.

That's it A+B+C = 1/4 -->A+B+C's 1 day work.

A's 1 day work = 1/16.
B's 1 day work = 1/12.
C's 1 day work = "We have A+B+C's 1 day work then subtraction to(A's 1 day+B's 1 day)".

= (A+B+C)-(A+B).
= (1/4)-(1/16+1/12).
= 1/4-(7/48) = 5/48.

C's 1 day work= 5/48 then C can do job= 48/5.

= Formula :: X 1 day task 1/n, x can do task n;

=48/5---> (9*5)+3/5---> 9 3/5.
=9 3/5.

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.

A can complete 1/16th of the work in 1 day.

B can complete 1/12th of the work in 1 day.

Let C complete 1/Xth of the work in 1 day.

So, A, B & C can complete (1/16 + 1/12 + 1/X)th part of the work in 1 day.

Therefore in 4 days, they together can complete = 4*(1/16 + 1/12 + 1/X)th part of the work . Always remember & denote work completed as 1.

On solving 4*(1/16 + 1/12 + 1/X) = 1, you can get the value of x which is the number of days taken by C to do the work.

Hope it helps you.

A - 16 Days.
B - 12 days.
A + B + C - 4 days.

We know A and B's one day work - 1/16 and 1/12.

Therefore, Add A+B = 1/16+1/12 (Take LCM).
= 7/48( Which is the one day work for A+B).

We know A+B+C's one-day work = 1/4.
So, A+B+C= 1/4,
7/48+C= 1/4, ( A+B= 7/48 )
C= 1/4 - 7/48 (Take LCM).
C= 5/48 (One day work).

Therefore C's Work = 48/5 (Just inverse of one day),
C= 9 * 3/5.

Consider A and B work alone.

1/16 + 1/12.
3/48 and 4/48.
That means A does work 3 units per day and B does 4 units per day.
So, now total work is done by A and B in one-day => 4 + 3 = 7 units per day
The total work is done by A and B in 4 days = 28 units.
Remaining units = 48-28 = 20 units.

That means 20 units work is done by C in 4 days in order to complete the work;
So, WORK DONE BY C IN ONE DAY = 20/4= 5 UNIT PER DAY,
C alone can do work in = 48/5 i.e 9(3/5).

You can solve all these sums very fast...

a can do the work in 16 days
b can do the work in 12 days
c can do the work in x days

Calc LCM of 16, 12 and x = 48x

units of work in a day by a = 48x/16 = 3x units
units of work in a day by b = 48x/12 = 4x units
units of work in a day by a = 48x/16 = 48 units

Total units of work in a day = 3x + 4x + 48= 7x+48
Thus in 4 days = 4(7x+48)= 28x+192

Total units of work=48x

Thus,
28x+192=48x
20x=192
x=9 3/5 days.

A very very simple solution than the provided as above.

A can complete a work in 16 days, B can complete the same work in 12 days and with the help of C together if they complete the work in 4 days, so assume total work to be done is 48. (LCM of 16, 12, 4).

Persons A B C | A+B+C.

Days- 16 12x = (48/5) = (9+3/5)4.

Work/day- 3 4 5 12 = 3+4+C.

Hence C = 5.

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Work - 48 48 48 48.

A work = 16 days.
B work = 12 days.

Total work was done by A and B = 48 unit (LCM Of A and B).

So work done by A in one day = 48/16= 3 unit.
And work was done by B in one day = 48/12 = 4 unit.

So work done by A and B in 1 day = 3+4 = 7 unit.
Work was done by A and B in 4 days = 7*4 = 28 unit.

So remaining work = 48-28 = 20 unit.
So work done by C in one day= 20/4 = 5 unit.

So, the total work was done by C in days = 48/5 days =9*3/5 days.