Question

a tank can be filled by two taps A and B in 6hours and 6hours respectively.the full tank can be emptied by tap C in 4 hours .if all the taps are working,how much time will it take to fill​

Answer 1

 Answer:

         12hrs

Step-by-step explanation:

time taken by tap A to fill tank= 6hrs

time taken by tap B to fill tank = 5hrs

time taken by tap C to empty tank = 4hrs

Work done by tap A = 1 / 6

Work done by tap B = 1 / 6

Work done by tap C = -1 / 4

Total work done by taps to fill the tank together

= 1 / 6 + 1 / 6 - 1 / 4

= 2 + 2 - 3 / 12

= 4 - 3 / 12

= 1 / 12

∴ Time taken by taps to fill the tank together = 12hrs

Answer 2

Given,

a tank can be filled by two taps A and B in 6hours and 6hours respectively. The full tank can be emptied by tap C in 4 hours .

Work done by tap A $= \frac{1}{6}$

Work done by tap B $=\frac{1}{6}$

Work done by tap C $=-\frac{1}{4}$

Total work done by tap to fill the tank together

$=\frac{1}{6}+\frac{1}{6}-\frac{1}{4}\\=\frac{2}{6}-\frac{1}{4}\\=\frac{8-6}{24}\\=\frac{2}{24}\\=\frac{1}{12}$

Therefore, the answer is $12$ hours.