1.

A tank has a leak which would empty the completely filled cistern in 20 hours. If the tank is full of water and a tap is opened which admits 2 liters of water per minute in the tank, the leak now takes 30 hours to empty the tank. How many liters of water does the tank hold?1). 24002). 45003). 12004). 7200

Answer»

Given data-

Let the total water holding capacity of cistern be x litres

A LEAK which would empty the completely FILLED cistern in 20 hours

⇒ Rate at which leak is taken PLACE= x/20 liter/hour→ 1

Water is admitted by a pump at the rate of 2 liters/ minute

⇒ Rate at which water is been admitted in cistern = 2× 60

⇒ Rate at which water is been admitted in cistern= 120 liters/ hour→2

When both process of leakage and water admission takes place simultaneously

Resultant rate of water leakage$( = \;\FRAC{x}{{20}} - 120)$→ 3

It takes 30 hours to empty the tanks with both actions takes place simultaneously

∴ after 30 hours of time water level in cistern will b 0

⇒ Original water level- total water leakage after 30 hours = 0

$(\begin{ARRAY}{l} \Rightarrow \;x - \;30 \times \;\left( {\frac{x}{{20}} - 120} \right) = \;0\\ \Rightarrow \;x - \frac{{30\left( {{\rm{x}} - 2400} \right)}}{{20}} = 0 \end{array})$

⇒ 2x = 3 (x – 2400)

⇒ 2x = 3x – 7200

⇒ x = 7200 liters


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