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two taps can together fill a tank in 3 1/3 hours.The tap of larger diameter takes 3 hours less than the smaller one to fill the tank separately. Find the time in which each type can separately fill the tank??

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Syeda answered 1 year(s) ago

Two water tap together can fill a tank in 75/8 hours. The tap of larger daimeter takes 10 hours less than the smaller one to fill the tank saparately. Find the time in which each tap can saparately fi

Two water tap together can fii a tank in 75/8hours. The tap of larger diameter taker 10 hours less than smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

Class-X Maths

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Asked by Aman

Jun 21

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Raghunath , SubjectMatterExpert

Member since Apr 11 2014

Sol :
Let the tap of the larger diameter fills the tank alone in (x – 10) hours.
 
In 1 hour, the tap of the  smaller diameter can fill 1/x part of the tank.
 
In 1 hour, the tap of the  larger diameter can fill 1/(x – 10) part of the tank.
 
Two water taps together can fii a tank in 75 / 8 hours.
 
But  in 1 hour the taps fill 8/75 part of the tank.
 
1 / x  +  1 / (x – 10) = 8 / 75.
 
( x – 10 + x ) / x ( x – 10) =  8 / 75.
 
2( x – 5) / ( x2 – 10 x) = 8 / 75.
 
4x2 – 40x = 75x – 375.
 
4x2 – 115x + 375 = 0
 
4x2 – 100x – 15x + 375 = 0
 
4x ( x – 25) – 15( x – 25) = 0
 
( 4x -15)( x – 25) = 0.
 
x = 25, 15/ 4.
 
But x = 15 / 4 then x – 10 = -25 /4 which is not possible since time
 
But x = 25 then x – 10 = 15.

Larger diameter of the tap can the tank 15 hours and smaller diameter of the tank can fill
the tank in 25 hours.