Question

M Malliy Idlik! Hours
. A tank can filled by two taps A and B in 12 hours and 16 hours respectively. The full tank
can be emptied by a third tap in 8 hours. If all the taps be turned on at the same time, in
how much time will the empty tank be filled up completely?​

Answer 1

$\huge\bold{\underline{QUESTION:}}$

A tank can filled by two taps A and B in 12 hours and 16 hours respectively. The full tank can be emptied by a third tap in 8 hours. If all the taps be turned on at the same time, in how much time will the empty tank be filled up completely?

$\huge\bold{\underline{\green{ANSWER:}}}$

Given:

$\mapsto$ Tap A can fill tank in 12 hrs.

$\mapsto$ Tap B can fill tank in 16 hrs.

$\mapsto$ Tap C can empty the tank in -8hrs

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$\implies$ Tap A's 1 hr work = 1/12

$\implies$ Tap B's 1 hr work = 1/16

$\implies$ Tap C's 1 hr work = -1/8

$\therefore$ Tap (A+B+C)'s 1 hr work = 1/12 + 1/16 - 1/8

= 7-6/48 = 1/48 = 48 hours

Hence, all the taps will take 48 hrs to fill the tank.

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Answer 2

Step-by-step explanation:

Given:

\mapsto↦ Tap A can fill tank in 12 hrs.

\mapsto↦ Tap B can fill tank in 16 hrs.

\mapsto↦ Tap C can empty the tank in -8hrs

_______________________________

\implies⟹ Tap A's 1 hr work = 1/12

\implies⟹ Tap B's 1 hr work = 1/16

\implies⟹ Tap C's 1 hr work = -1/8

\therefore∴ Tap (A+B+C)'s 1 hr work = 1/12 + 1/16 - 1/8

= 7-6/48 = 1/48 = 48 hours

Hence, all the taps will take 48 hrs to fill the tank.

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