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Home » Two water taps together can fill a tank in 75/8. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.
Two water taps together can fill a tank in 75/8. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.
CBSE | Class 10 | Exercise 4.3 | Quadratic Equations
Two water taps together can fill a tank in 75/8. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

Solution:

Let the time taken by the smaller pipe to fill the tank = x hr.

Time taken by the larger pipe = (x – 10) hr

Part of tank filled by smaller pipe in 1 hour = 1/x

Part of tank filled by larger pipe in 1 hour = 1/(x – 10)

As given, the tank can be filled in

    \[~9\frac{3}{8}=\text{ }75/8~hours\text{ }by\text{ }both\text{ }the\text{ }pipes\text{ }together.\]

Therefore,

1/x~+\text{ }1/x-10\text{ }=\text{ }8/75

x-10+x/x\left( x-10 \right)\text{ }=\text{ }8/75

\Rightarrow 2x-10/x\left( x-10 \right)\text{ }=\text{ }8/75

\Rightarrow 75\left( 2x~\text{ }10 \right)\text{ }=\text{ }8{{x}^{2}}~\text{ }80x

\Rightarrow 150x~\text{ }750\text{ }=\text{ }8{{x}^{2}}~\text{ }80x

\Rightarrow 8{{x}^{2}}~\text{ }230x~+750\text{ }=\text{ }0

\Rightarrow 8{{x}^{2}}~\text{ }200x~\text{ }30x~+\text{ }750\text{ }=\text{ }0

\Rightarrow 8x\left( x~\text{ }25 \right)\text{ }-30\left( x~\text{ }25 \right)\text{ }=\text{ }0

\Rightarrow \left( x~\text{ }25 \right)\left( 8x~-30 \right)\text{ }=\text{ }0

\Rightarrow ~x~=\text{ }25,\text{ }30/8

Time taken by the smaller pipe cannot be 30/8 = 3.75 hours, as the time taken by the larger pipe will become negative, which is logically not possible.

Therefore, time taken individually by the smaller pipe and the larger pipe will be 25 and 25 – 10 =15 hours respectively.

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