Aptitude - Pipes and Cistern - Discussion

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.

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.

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.

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.

Let's take tank capacity as 42 litres.
Given A+B+C finishes in 6 hours.

Per hour, A+B+C= 42/6 = 7 litres/hour.
But, They worked together for only 2 hours.

For 2 hours,
A+B+C= 7 litres => 2 hours=14litres/2hrs.
Remaining= 28 litres.

(A+B) worked to finish it in 7 hours.
So, (A+B)= 28/7 = 4 litres/hour.

Normally, (A+B)+C= 42/6 = 7 litres/hr.
In this one hour, (A+B) will fill 4 litres.

Remaining 3 litres will be filled by C in 1 hour.
So, C alone = 42/3= 14 hours.

@All.

Here, I've taken tank capacity as 42 litres.
A + B + C = 6 hours.
Remaining part by A + B in 7 hours.
So, LCM of 6 and 7 is 42.
If we take LCM's, cancellations will be easy in further steps.

This can be easily solved.
1/A + 1/B + 1/C = 1/6.
1/A + 1/B = 1/6 - 1/C.

Therefore, a+b+c worked for 2hrs + a+b worked for 7hrs ( a+b=1/6 - 1/c) = Total work i.e., 1
i.e., 2(1/6) + 7(1/6 - 1/C ) = 1.
2/ 6 - 7/6 -1 = 1/C.
c = 14.

How 1/6 - 2/21 = 1 /14? Explain please.

It can be done very easily by the LCM method. Let the capacity of cistern be 42 units LCM of 6, 2 , 7. Then according to question.

A+B+C fills 7 units per hour(42/6). hence in 2 hours of operation, they fill 14 units.

Remaining units 42"14 = 28, which A+B fills in 7 hours means A+B fills 4 units per hour. hence it is clear that C fills 3 units per hour. So, C will fill the cisterns i.e. 42 units in 42/3 = 14 Hours.

It can be done very easily by the LCM method. Let the capacity of cistern be 42 units LCM of 6, 2 , 7. Then according to question.

A+B+C fills 7 units per hour(42/6). hence in 2 hours of operation, they fill 14 units.

Remaining units 42"14 = 28, which A+B fills in 7 hours means A+B fills 4 units per hour. hence it is clear that C fills 3 units per hour. So, C will fill the cisterns i.e. 42 units in 42/3 = 14 Hours.