Aptitude - Pipes and Cistern - Discussion

A+B+C=6hr-------6ltr TC------1ltr/he fill tank.
A+B+C can run 2hr only - 2 LTR tank fill both.

Remaining part 6 - 2 = 4.

Now C is closed after 2he now remaining part fill A+B in 7hr.

So A+B = fill 4ltr ----7hr , so 1hr---4/7 effi, C efficiency is 3/7, So C can fill the tank Alone 6/3/7 = 14.

Assume total work = 6.
So, efficiency of a + b + c = 1.
We know w = e * t.
w = 1 * 2 {given}
= 2.

Balance = 4 work.
a + b = 4 work.
w = e * t.
4 = e * 7.
e = 4/7.

Then c = 1 - 4/7 = 3/7.
c alone = 6/3/7 = 14 hrs.

Let C alone can fill the tank in x hours.

2 hours work of A,B & C + 7 hours work of A & B = 1,
According to the condition,
2/6 + 7(1/6 - 1/x) = 1,
2/6 + 7 (x - 6/6x) = 1,
2/6 + 7x - 42/6x = 1,
2x + 7x - 42/6x = 1,
9x - 42 = 6x,
9x - 6x = 42,
3x = 42,
x = 42/3,
x = 14.

Take,total hrs =total work.

A+B+C=6hrs(total hrs)=6 work(total wrk).
A+B +C work for 2hrs so 2work completed.
Remaining work (6-2) is 4.

Remaining wrk completed by A+B in 7hrs.
A+B=4/7 work/hrs.

Therefore, C's efficiency 1-(4/7)=3/7 wrk/hrs.

C-----alone---total work/efficiency.
6/(3/7) = 14 hrs.

Not getting this, please explain it.

Part filled in 2 hours = 2/6 = 1/3. Remaining part = 2/3.
(A + B)'s 7 hours' work = 2/3.
So, (A+B)'s 1 hr work = 2/21,

Therefore C's 1 hour's work
= [(A+B+C)'s 1 hour]-[(A+B)'s 1 hr work].
=(1/6 - 2/21) = 1/14.
C alone can fill the tank in 14 hours.

first understand the question properly.

A, B, C all opened can fill in 6 hours.
ie 1/A+1/B+1/C=1/6________(x)
ie 1/6th of tank is filled if all the three operate for an hour.
So if all 3 operate for 2 hours 2/6th of the tank is filled.
So remaining is 2/3rd.(1-2/6).

After 2 hours, C is closed.
to fill the 2/3rd by A & B it takes 7 hours.
[to find the time by c alone we need to find 1/A+1/B to substitute in (x)..]
So A and B in 1 hour can complete 2/(3*7).
ie 1/A+1/B=2/21. sub in x.
1/C=1/6-2/21.
We get 1/C =1/14.
So, C takes 14 hours to fill the tank.

Please tell me, how to solve this question using LCM method?

Why did you divide 42 by 3?

And how?

1/A+1/B+1/C=1/6,
1/A+1/B=1/7.
1/6-1/7=1/42,
42/3=14.