Question

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​

Answer 1

Answer:

Let t = the time to the fill the tank 

t/30 + t/40 + t/60= 1 

40X60t +30X60t +30X40t = 30X40X60 

24t.+18t + 12t = 120X6 

4t+ 3t + 2t = 120 

9t= 120 

t =120/9 

t =13 minutes and 3/9*60 

= 13minutes and 20 seconds

Answer 2

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