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An outlet pipe can empty a tank in 24 hours. A pipe that fills the tank at a rate of 2 ltr/min is opened together with the outlet pipe and the tank gets filled in 16 hours. What is the capacity of the tank?1. 1152 ltr2. 1000 ltr3. 1252 ltr4. 2000 ltr5. 1352 ltr |
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Answer» Correct Answer - Option 1 : 1152 ltr GIVEN: Time taken by outlet pipe to empty = 24 hours Time taken by both inlet and outlet pipes to fill = 16 hours Rate of filling of inlet pipe = 2 ltr/min EXPLANATION: Time taken by outlet pipe to empty = 24 hours Time taken by both inlet and outlet pipes to fill = 16 hours LCM of 24 and 16 is 48 so, let the capacity of the tank be 48 units Per hour efficiency of outlet pipe = \(\frac{48}{24}= -2\) units/hour (here '-' sign indicates outlet) Per hour efficiency of both pipes together = \(\frac{48}{16}=3\) units/hour Per hour efficiency of inlet pipe = Per hour efficiency of both pipes together - Per hour efficiency of the outlet pipe \(\Rightarrow 3-(-2)=3+2=5 units/hour\) 5 units/hour = \(\frac1{12}\) units/min \(\frac1{12}\) units/min = 2 ltr/min \(\frac1{12}\) units = 2 ltr 1 unit = 24 ltr Capacity of tank 48 units = 48 \(\times\) 24 = 1152 ltr |
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