consider a tank with 1 litre(or keep some quantity as u wish) of capacity. now to fill 1 litre it takes 3 hrs(180 mins). if the tank has a hole then it takes 3 1/2 hrs(210 mins) but remember it does not hav a quantity of 1 litre bcoz of hole(as some more water is wasted due to leakage). so (1 litre + x ). In 1 min the ideal tank gets filled up with 1/180 litre. In 1min the tank with hole gets filled with (1+x)/210 litre. now our aim is to find x litres due to leakage. therefore x litre is leaked in 3 1/2 hrs. (1/210)+(x/210)-(1/180) 1min - 1min 0 (1/210)-(1/180) -(x/210) after solving x 1/6 x 1/6 litre is leaked in 3 1/2 hrs. then 1 litre 3 1/2 * 621 hrs
Ans is 21 hrs A tap can fill in 3 hrs and leak in x hrs In 1 hr the tap can fill 1/3 of the tank In 1 hr it can leak 1/x of the tank Thus in 1 hr it can totally fill 1/3-1/x (x-3)/3x Thus the tap can fill the entire tank in 3x/(x-3) 3x/x-3 3.5 x 21
Let the tank be 1 ltr. It takes 180 min(3 hr) to fill this tank. Hence 1 min's work is 1/180 After the tank got a hole in it it takes 3 and 1/2 hrs ie.. 210 min. hence work expended in 210 min is 210*1/180 7/6 Hence extra work spended due to hole is 7/6-1 1/6. To compensate this 1/6th(corresponding to wasted water) took 3 and 1/2 hrs. So time taken for entire tank to get emptied is 210*6 1260min 1260/60 21 hrs.
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