Question

16 taps are fitted to a water tank. Some of them are water
taps to fill the tank and the remaining are outlet taps
used to empty the tank. Each water tap can fill the tank in
6 hours and each outlet tap can empty it in 18 hours. On
opening all the taps, the tank is filled in 1
hours. Find
the number of empty taps.
a) 7
b) 9
c) 6
d) 8
9 tans are fitted​

Answer 1

Answer:

d) 8 is the correct answer.

Step-by-step explanation:

Number of inlet taps = x

then Number of outlet Taps = 16 - x

Each water Tap fill in 6 hrs

=> x  water tap fill in 6/x  hrs

=> filled in 1hr by x taps   = x/6

Each outlet tap can empty in 18 hrs

=> 16 -x Taps can empty in 18/(16 - x)  Hr

filled in 1hr by 16-x taps    = (16-x)/18

Tank is filled in 12 hrs

Tank filled in 1 hrs = 1/12

=>  x/6  - (16 - x)/18   = 1/12

multiplying by 36 both sides

=> 6x  - 2(16 - x) = 3

=> 6x - 32 + 2x = 3

=> 8x = 64

=> x = 8

$8 \: taps \: will \: be \: empty.$

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