Aptitude - Time and Work - Discussion

Good and clear explanation. Thanks all.

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.

Why is 5/48 take as its reciprocal? Please explain to me.

The work is completed by A in 16 days and by B in 12.

LCM of 16 and 12 is 48.(Total work is also 48).
The efficiency of A= 48/16=3 and B= 48/12=4,

They complete the work in 4 days.
Total work/time = Efficiency.
48/4 = 12(Efficiency of A+B+C = 12).
The efficiency of A+B is 3+4=7
The efficiency of C is 12 - 7 = 5.

Total work/Efficiency = Time.

48/5 = 9.6 is also written as (9*3/5).

@Nil.

It's a fractional rule.

48/5 = 9+3/5.
Let me explain.

=> 5x9 = 45
So, you can say the reminder a numerator and the denominator is also a denominator.
The reminder is 3 and the Denominator is 5.

So, 9*3/5..

A = 16
B = 12.

A + B + C = 4.
16,12,4 LCM = 48.
then,16/48 = 3.
12/48 = 4.
4/48 = 12.
Then,C - (A + B) = 12-(3+4) = 5.
then 48/5.

A --- 15.
B --- 20.

We took LCM -- 60.
15 * 4 = 60.
20 * 3 = 60.

Work done = 4 days * 7 = 28 units of work.
60 - 28 = 32,
Part left = 32/60,
8/32.

Can also be done like this;

(1/16) *4+ (1/12) * 4 + (1/x) * 4 = 1 (as the total work is 1).

Everybody together completes 1/4 of work in one day.

So, (1/4)*4 = 1.

A = 16.
B = 12.
A + B + C = 4.

Total work by a, b, c ie LCM of 16, 12, 4 = 48.

Then A work in 1 day = 48/16 = 3unit.
and B work in 1 day = 48/12 = 4 unit.

And A +B+C work in 1 days = 48/4= 12 unit.
Therefore put value of a and b ie 3 + 4 + c = 12.
ie c work in 1 day = 5 unit.
Therefore total work done by C is 48/5 ans simple and fast method.

Thanks all for helping me to get the answer.