6. A water tank is filled by a tap from above while it is emptied by another tap at the bottom. If the above tap fills with the speed of 25 litres per hour and the bottom tap drains it with the speed of 10 litres per hour. After 4 hours what will be the amount of water left in the tank (imagine initially the tank was empty)?
Answers & Comments
[tex]∴ Above \: tap \: fills \: in \: 4 \: hour \\ \\ = 25 × 4 \: litre \\ \\ = 100 \: litre \: water[/tex]
[tex]Again, \: bottom \: tap \: drains \\ in \: 1 \: hour \\ \\ = 10 \: litre \: water[/tex]
[tex] ∴ Bottom \: tap \: drains \: in \: \\ 4 \: hour \\ \\ = 10 × 4 \: litre \\ \\ = 40 \: litre \: water[/tex]
[tex] ∴ Amount \: of \: water \: in \: tank \: \\ after \: 4 \: hour \\ \\ = 100 \: litre – 40 \: litre \\ \\ = 60 \: litre [/tex]
[tex]Therefore, \: there \: is \: 60 \: litre \\ water \: in \: a \: tank \: after \\ 4 \: hour[/tex]
∴Above tap fills in 4 hour
= 25 x 4 litre
= 100 litre water
Again, bottom tap drains in 1 hour
= 10 litre water
∴Bottom tap drains in 4 hour
= 10 × 4 litre
= 40 litre water
∴Amount of water in tank after 4 hour
= 100 litre-40 litre
= 60 litre
Therefore, there is 60 litre water in a tank after 4 hour