Verified answer

Answer:

15

Step-by-step explanation:

Thus, in 1 hour the taps fill 8/75 part of the tank. Time can never be negative so x = 15/4 is not possible. ∴ The tap of smaller diameter can separately fill the tank in 25 hours, and the time taken by the larger tap to fill the tank = ( 25 – 10 ) = 15 hours.

Step-by-step explanation:

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Question

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Two water taps together can fill a tank in 9

8

3

hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time(in hrs.) in which tap of smaller diameter can separately fill the tank.

Medium

Solution

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Correct option is A)

Consider that the tap with smaller diameter fills the tank in x hours.

Then, the tap with larger diameter fills the tank in x−10 hours.

This shows that the tap with a smaller diameter can fill

x

1

part of the tank in 1 hour. Similarly, the tap with larger diameter can fill

x−10

1

part of the tank in 1 hour.

It is given that the tank is filled in

8

75

hours that is, the taps fill

75

8

part of the tank in 1 hour. Then,

x

1

+

x−10

1

=

75

8

x(x−10)

x−10+x

=

75

8

x

2

−10x

2x−10

=

75

8

75(2x−10)=8(x

2

−10x)

150x−750=8x

2

−80x

8x

2

−230x+750=0

4x

2

−115x+375=0

4x

2

−100x−15x+375=0

4x(x−25)−15(x−25)=0

(4x−15)(x−25)=0

4x−15=0

x=

4

15

Or,

x−25=0

x=25

When x=

4

15

, then, x−10=

4

15

−10

=

4

15−40

=−

4

25

This cannot be possible because time can never be negative.

When x=25, then,

x−10=25−10

x=25

Therefore, the tap of smaller diameter can separately fill the tank in 25 hou