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sabbavarapu madhu

· started a discussion

· 1 Months ago

answer (Question: 109962.0 )

why we should multiply only with 55 and not with others

Question:

Two taps A and B can fill a cistern in 20 and 30 minutes respectively whiles third pipe C can empty the tank in 15 minutes. If the three taps are opened successively for one minute each. How long will it take to fill the cistern ?

Options:
A) 165 minutes
B) 167 minutes
C) 168 minutes
D) 169 minutes
Solution:
Ans: (b) Work of three pipes for 3 minutes (one minute’s work of each pipe)

\(=\cfrac{1}{20}+\cfrac{1}{30}-\cfrac{1}{15}=\cfrac{3+2-4}{60}=\cfrac{1}{60}\)

\(\therefore\) Work of these pipes for 55 minutes each \(=\cfrac{1}{60}\times55=\cfrac{11}{12}\)

Total time = 3 x 55 = 165 minutes

\(\therefore\) Remaining part to be filled \(=1-\cfrac{11}{12}=\cfrac{1}{12}\)

Tap A will fill \(\cfrac{1}{20}\) of the cistern in the next 1 minute.

\(\therefore\) Remaining portion to be filled by tap B \(=\cfrac{1}{12}-\cfrac{1}{20}=\cfrac{2}{60}=\cfrac{1}{30}\)

Time taken by tap B to fill \(\cfrac{1}{30}\) of the cistern \(\cfrac{1}{30}\times30=1\) minute

Hence total time taken = 165 + (1 + 1) = 167 minutes

Knowledge Expert

· commented

· 1 Months ago

Dear student,
We have updated the solution, please go through it.
Keep learning,
Team TR

Vaibhav Yadav

· commented

· 1 Months ago

its because if this:-
you cannot multiply by 57 or greater ( in that case the tank is already filled at some point before in time)
now is you consider 56 then what you are doing is 60-4=56 litres, means the tank is full one-minute ago. ( you are withdrawing 4 litres in last mintues).
so only option left is 55.
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