Two water taps together can fill a tank 9 and 3/8 hours. The tap of larger diameter takes 10 hour less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.’
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Given:-
To Find:-
The time in which each tap can separately fill the tank.
Assumption:-
Let the time taken by smaller tap to fill the tank be x
Time taken by larger tap to fill the tank =
Solution:-
In one hour tank filled by smaller tap =
In one hour tank filled by larger tap =
Total time taken by both the taps to fill the tank =
In one hour tank filled by both the taps =
ATQ,
=
=
By Cross multiplication,
=
Taking all the variables on LHS,
The sign will change as follows:-
(-) into (+)
(+) into (-)
=
=
=
Taking -2 as common,
=
=
By splitting the middle term,
=
=
=
Either,
=
Or,
=
=
Taking x = 25
Time taken by smaller tap to fill the tank = x = 25 hours
Time taken by larger tap to fill the tank = x-10 = 25 - 10 = 15 hours.
Taking x =
Time taken by smaller tap to fill the tank = x =
Time taken by larger tap to fill the tank = x - 10 =
=
=
As negative time cannot be taken,
Hence,
Time taken by smaller tap = 25 hours
Time taken by larger tap = 15 hours.
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