A tap can fill a tank in 24 hours and an outlet can empty the full tank in 30 hours. In how many hours the empty tank will be filled, if both the tap and the outlet are opened simultaneously?

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Solution

Tap fill $= 24 h r s (+)$

for $1 h r = \frac{1}{24}$ fill

Tap empty $= 30 h r s (-)$

for $1 h r = {\frac{1}{30}}^{t h}$ empty

ln $1 h r = \frac{1}{24} - \frac{1}{30} = \frac{5 - 4}{120} = {(\frac{1}{120})}^{t h}$

$∴ I t t a k e s 120 h r s t o f i l l t h e t a n k$

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A tap can fill a tank in 24 hours and an outlet can empty the full tank in 30 hours. In how many hours the empty tank will be filled, if both the tap and the outlet are opened simultaneously?

Tap fill =24 hrs(+)for 1 hr=124 fillTap empty =30 hrs(−)for 1 hr=130th emptyln 1 hr=124−130=5−4120=(1120)th∴ It takes 120 hrs to fill the tank

Tap fill $= 24 h r s (+)$

for $1 h r = \frac{1}{24}$ fill

Tap empty $= 30 h r s (-)$

for $1 h r = {\frac{1}{30}}^{t h}$ empty

ln $1 h r = \frac{1}{24} - \frac{1}{30} = \frac{5 - 4}{120} = {(\frac{1}{120})}^{t h}$

$∴ I t t a k e s 120 h r s t o f i l l t h e t a n k$