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One pipe can fill a tank in 3 hours less than another. The two pipes together can fill the tank in 6 hours 40 minutes, then the time each pipe will take to fill the tank is:

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15 hours, 12 hours

25 hours, 12 hours

15 hours, 2 hours

15 hours, 20 hours

answer is A.

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Detailed Solution

Given that,
One pipe can fill a tank in 3 hours less than another.
The two pipes together can fill the tank in 6 hours 40 minutes.
Since, 1hours=60minutes then,
6 hours 40 minutes

= 6 \frac{40}{60} hours = \frac{20}{3} hours

.
Let the pipes can fill the tank in

x

hours and (

x − 3

) hours .
Now, according to the question,

1 x + 1 x − 3 = 320 ⇒ x − 3 + x x x − 3 = 320 ⇒ 40 x − 60 = 3 x 2 − 9 x ⇒ 3 x 2 − 49 x + 60 = 0

…(1)
We know that quadratic formula for the general equation

a x^{2} + by + c = 0

x = \frac{- b \pm \sqrt{b^{2} - 4 ac}}{2 a}

.
Then using quadratic formula in equation (1),

x = \frac{- (- 49) \pm \sqrt{{(- 49)}^{2} - 4 (3) (60)}}{2 (3)}

\Rightarrow x = \frac{49 \pm 41}{6}

On taking positive value,

\Rightarrow x = \frac{49 + 41}{6}

\Rightarrow x = \frac{90}{6}

\Rightarrow x = 15

On taking negative value,

\Rightarrow x = \frac{49 - 41}{6}

\Rightarrow x = \frac{8}{6}

\Rightarrow x = 1.33

The decimal value of x=1.33 is neglected because at x=1.33,

(x - 3) < 0

.
So,

x = 15

hours
Then,

x - 3 = 15 - 3

\Rightarrow 12

hours
Then, time each pipe will take to fill the tank are 15 hours and 12 hours.
Hence, option 1 is correct.

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