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A water pump takes 6 hours to fill an overhead tank class 8 maths CBSE

Hint

This problem is similar to those problems in which the working persons, their working hours and number of days they work would be given. This is also similar to it. So we will first find the total work done and then the work done by the two pipes in one hour. According to that we will calculate the work done by the first pipe in 2 hours and then the remaining work to be completed by the standby pipe.

Complete step-by-step answer

Let the first pump be A and the standby pump be S. Now pipe A takes 6 hours to fill an overhead tank. Standby pump S takes 10 hours to fill the same tank. Now the LCM of these hours will be the total capacity of the tank we can say. So the capacity is 60. Now pump A completes 60 6=10 w o r k/h r And pump S completes 60 10=6 w o r k/h r That is pump S is slower. Anyways ! Now we started with pump A for the first two hours. So it will fill 2×10=20 w o r k of the total capacity. Now pump S is in work. So it needs to fill 60−20=40 w o r k. But it can do 6 w o r k/h r. So the time taken by it to complete the rest of the work is, 40 6=6.6 6¯h r s This is the time the standby pump took.

So, the correct answer is “6.6 6¯h r s”.

Note

Here note that the pump A takes lesser times than pump S. so we can conclude here that the work done and the time are inversely proportional. Such that in less time pump A completes more work. Sometimes the proportion is not inverse in some cases. Like the wages paid for hours of working. The more a person works, the more he gets paid.