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Grade: 12th Pass

                        

Two water taps together can fill a tank in 75/8 hrs. The top of larger diameter takes 10 hr. less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

9 years ago

Answers : (1)

Sudheesh Singanamalla
114 Points
							

Suppose that the faster pipe takes x hours to fill the tank

slower pipe will take x+10 hours to fill the tank

since faster tap (larger diameter tap) takes x hours to fill the tank,

portion of tank filled in  1 hour = 1/x

portion of tank filled in 75/8 hours = 75/8x --------------------(i)

similarly portion of tank filled by slower pipe in x+10 hours to fill the tank is 1/(x+10)

portion of tank filled in 75/8 hours = 75/[ 8* (x+10) ] -----------------------(ii)

it is given that the tank is filled in 75/8 hours

so

75/8x + 75/[ 8* (x+10) ] = 1

taking 75/8 common outside and moving it to the RHS we get

1/x + 1/(x+10) = 8/75

( x + 10 + x )/ x(x+10) = 8/75

75 * (2x + 10) = 8 * (x2+10x)

150x + 750 = 8x2 + 80x

8x2 - 70x - 750 = 0

dividing by 2

4x2 - 35x - 375 = 0

 

now solve the equation and ignore the negative answer obtained !

you will get the time taken by the tap of larger diameter, add 10 to it and you will get the time taken by the smaller diametered tap

 

 

PLEASE APPROVE !

 

9 years ago
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