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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 tar
can separately fill the tank.
Answers
Answer:
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Answer:
consider the time taken by the smaller diameter tap = x
The time is taken by the larger diameter tap = x – 10
Totaltimeistakentofillatank=938
Total time is taken to fill a tank = 75/8
In one hour portion filled by smaller diameter tap = 1/x
In one hour portion filled by larger diameter tap = 1/(x – 10)
In one hour portion filled by taps = 8/75
⇒ 1x+1x−10=875 x−10+xx(x−10)=875 2x−10x2−10x=875
75 (2x-10) = 8(x2-10x)
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