Pipe P alone can fill the tank in 18 hours and pipe Q alone can fill the tank in 12 hours. Both pipes opened for 7 hours. The fraction of the tank remained after 7 hours is equal to the fraction of the tank filled by pipe R in one hour. In what time the tank gets filled when all three pipes are opened simultaneously?

7 hours
4 hours
3 hours
9 hours
6 hours

LohaHridoy

6 views

2025-01-04 04:42

1 Answers

AhmedNazir

Option 5 : 6 hours

Given:

Pipe P's 1 hour's work = 1/18

Pipe Q's 1 hour's work = 1/12

Calculation:

Pipe (P + Q)’s 1 hour's work = 1/18 + 1/12 = 5/36

Pipe (P + Q)’s 7 hours work = 7 × 5/36 = 35/36

⇒ Remaining work = 1 – 35/36 = 1/36

Then,

⇒ 1/36 × R = 1

⇒ R = 36

Pipe R's 1 hour's work = 1/36

⇒ Pipe (P + Q + R)’s 1 hour's work = 1/18 + 1/12 + 1/36 = 1/6

∴ It will take 6 hours to fill the tank when all three pipes are opened simultaneously.

6 views Answered 2022-09-04 04:29

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