8
9. Two water taps together can fill a tank in 9 hours. 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.
Answers
Answer:
Answer:
Let the tap with smaller diameter fills the tank alone in x hours
Let the tap with larger diameter fills the tank alone in (x – 10) hours.
In 1 hour, the tap with a smaller diameter can fill 1/x part of the tank.
In 1 hour, the tap with larger diameter can fill 1/(x – 10) part of the tank.
The tank is filled up in 75/8 hours.
Thus, 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
2x – 10/x(x-10) = 8/75
75 (2x-10) = 8(x2-10x) by cross multiplication
150x – 750 = 8x2 – 80x
8x2 − 230x + 750 = 0
4x2−115x + 375 = 0
4x2 − 100x −15x + 375 = 0
4x(x−25)−15(x−25) = 0
(4x−15)(x−25) = 0
4x−15 = 0 or x – 25 = 0
x = 15/4 or x = 25
Case 1: When x = 15/4
Then x – 10 = 15/4 – 10
⇒ 15-40/4
⇒ -25/4
Time can never be negative so x = 15/4 is not possible.
Case 2: When x = 25 then
x – 10 = 25 – 10 = 15
∴ 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.
Answer:
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Step-by-step explanation:
Let the tap with smaller diameter fills the tank alone in x hours
Let the tap with larger diameter fills the tank alone in (x – 10) hours.
In 1 hour, the tap with a smaller diameter can fill 1/x part of the tank.
In 1 hour, the tap with larger diameter can fill 1/(x – 10) part of the tank.
The tank is filled up in 75/8 hours.
Thus, 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
2x – 10/x(x-10) = 8/75
75 (2x-10) = 8(x2-10x) by cross multiplication
150x – 750 = 8x2 – 80x
8x2 − 230x + 750 = 0
4x2−115x + 375 = 0
4x2 − 100x −15x + 375 = 0
4x(x−25)−15(x−25) = 0
(4x−15)(x−25) = 0
4x−15 = 0 or x – 25 = 0
x = 15/4 or x = 25
Case 1: When x = 15/4
Then x – 10 = 15/4 – 10
⇒ 15-40/4
⇒ -25/4
Time can never be negative so x = 15/4 is not possible.
Case 2: When x = 25 then
x – 10 = 25 – 10 = 15
∴ 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.
