a water tank has 3 inlets , inlets A alone can fill the tank in 30 min inlet B can fill it in 40 min inlet C can fill it in 60 min if all the 3 inlets are opened together , how long will it take to fill the tank
Answers
Answer:
A's 1min work =1/30
B's 1min work=1/40
C's 1min work=1/60
(A+B+C)'s 1 min work=1/30+1/40+1/60
=90/120=3/4
Hence,tank will be filled in =1÷3/4 hrs=4/3hrs=80min
follow plz
Step-by-step explanation:
Let the Tank to be Filled be : T
Given that A Inlet alone can fill the Tank in 30 mins
⇒ In One Minute A Inlet fills T/30 of the Tank
Given that B Inlet alone can fill the Tank in 40 mins
⇒ In One Minute B Inlet fills T/40 of the Tank
Given that C Inlet alone can fill the Tank in 60 mins
⇒ In One Minute C Inlet fills T/60 of the Tank
⇒ In One Minute A - B - C inlets Fill : T/30 + T/40 + T/60
⇒ T/30 + T/40 + T/60 = (4T + 3T + 2T)/120 = 9T/120 = 3T/40
⇒ In One Minute A - B - C inlets Fill : 3T/40
⇒ In 40/3 Minutes A - B - C inlets Fill : 3T/40 × 40/3
⇒ In 40/3 Minutes A - B - C inlets Fill the Tank 'T'
⇒ 40/3 = 13 + 1/3 = 13 minutes and 60/3 seconds
⇒ 40/3 = 13 Minutes and 20 seconds
⇒ The A - B - C inlets Together fill the Tank in 13 Minutes and 20 seconds