Question

Pipe A takes 24 minutes to fill a tank. Pipe B takes 32 minutes to fill the same tank. if both the pipes are opened simultaneously, after how much time should pipe A closed so that it takes 16 minute to fill the tank.​

Answer 1

Step-by-step explanation:

Let the total capacity of the tank be 96 units (LCM of 24 & 32).

• The rate of filling of water by pipe A = $\frac{96}{24}$ = 4 units per minute.

• The rate of filling of water by pipe B = $\frac{96}{32}$ = 3 units per minute.

=>Since pipe A is open for 18 minute water filled by it =16 × 4= 64 units

=>Water filled by pipe B = 96 - 64 = 32 units.

So, the time for which it was open = $\frac{32}{4}$ = 8minutes.

Hence the pipe A must be closed after 8 minutes for the tank to be filled in 16 minutes.

Answer 2

The correct answer is 20 min.

Part filled by A in 1 min = 1/24

Part filled by B in 1 min = 1/32

Therefore,

x (1/24+1/32) + (9 - x) × 1/24 = 1

x (4+3/96) + (9-x)/4 = 1

7x/96 + (9-x)/24 = 1

7x + 4 (9-x)/96 = 1

7x + 4 (9-x) = 96

7x + 36 - 4x = 96

7x - 4x = 96 - 36

= 3x = 60 x = 60/3 = 20

Hence, A pipe must be closed after 20 min