Tap A can fill the cistern in 40 hours and tap B is an inlet pipe with

Question

Tap A can fill the cistern in 40 hours and tap B is an inlet pipe with water flowing at the rate of 12 litres per hour. At first the tap A is Opened and after 6 hours tap B is also opened. After 10 hours of opening tap B, tap A is shut. If the tank get completely filled exactly after 26 hours after tap A was shut, find the capacity of the tank

(A) 500

(B) 720

(C) 800

(D) 660

(E) 540

(A) 500

(B) 720

(C) 800

(D) 660

(E) 540

PikaB · Answer

The first value of no of hours for A is missing i think.

rsrighosh · Answer

Bunuel 
How to proceed with this question?

IanStewart · Answer

I've highlighted a typo in the question -- there's a number missing, which makes it unanswerable. I suspect the missing number is "6", assuming it's not a fractional value, since no other integer will lead to an integer answer in the range of the answer choices, and 6 does lead to an answer choice. The wording is very awkward, but assuming '6' is the missing number, we know these three things happen in sequence:

Tap A is on for 6 hours.
Taps A and B are both on for 10 hours.
Tap B is on for 26 hours

Since A is on for 16 hours, and A fills the whole tank in 40 hours, then A fills 16/40 = 2/5 of the tank while it is on. So B fills the rest, or 3/5 of the tank, while it is on. B is on for a total of 36 hours, filling 12 litres each hour, so B fills 36*12 litres. That's 3/5 of the tank, so the entire tank is (5/3)(36*12) = 5*144 = 720 litres in capacity.

Bunuel · Answer

Edited the question. My bad. Thank you!

MDHAKAN1 · Answer

A works for 16 hours and fills 2/5 of the cistern=rate*time=(1/40)*16
B works for 36 hours and fills the remaining (3/5)x of the cistern= 1x-(2/5)*x
therefore B, rate*time=work: 12*36=(3/5)*x, solving which we get 720

pierjoejoe · Answer

the problem can be solved knowing that 
A has a rate of x liters per 40 hour 
 -->  Rate(a)  = x/40
B has a rate of 12 liters per hour 
 -->  Rate(b)  = 12
A and B together have a rate of 
 -->  Rate(a+b)  = 12 + x/40

now, knowing that the total work to do is x, and that the work in a certain section is simply time multiplied by rate:
 6*Rate(a)  +  10*Rate(a+b)  +  26*Rate(b)  = x

A works alone for 6h 
 -->  6 * Rate(a)  = 6*(x/40) =  6x/40 
A and B together for 10 hours
 -->  10*Rate(a+b)  =10 * (12 + x/40) =  120 + 10x/40 
B works alone for 26 hours 
 -->  26*Rate(b)  = 26 * 12 =  432

6x/40 + 120 + 10x/40 +432 = x

find x = 720

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Tap A can fill the cistern in 40 hours and tap B is an inlet pipe with

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