tap A fills a tank in 6 hours tap B fills it in 8 hours and tap C empties it in 10 hours. starting with an empty tank and all the three taps are opened find how long it takes to fill the tank?​

It will take 5 hours and 5 minutes to fill the tank

Step-by-step explanation:

Here, we want to get the time taken to fill the tap

Let us have the rate per hour

A fills in 6 hours; so the fraction filled in an hour is 1/6

B fills in 8 hours, so the fraction filled in an hour is 1/8

C empties in 10 hours, so the fraction removed per hour is 1/10

So factoring the supply and removal, where removal is on a negative basis

we have it that in an hour, the fraction retained is;

1/6 + 1/8 - 1/10

= (20 + 15 - 12)/120

= 23/120

So this is the fraction retained per hour

The number of hours it will take to have a whole is simply the reciprocal of this fraction

That would simply be 120/23 = 5 5/23

5 hours and 5 minutes