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Q.

Two water taps together can fill a tank in 75/8 hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time (in hours) in which a tap of smaller diameter can separately fill the tank.


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a

25

b

-25/4

c

24

d

25/4 

answer is A.

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Detailed Solution

Concept- We'll use the idea of how much of the tank gets filled in an hour in this case.
Let us assume that the tap with smaller diameter can separately fill the tank in xx hours.
According to the problem statement it is given that the tap with larger diameter can separately fill the tank in (x-10) hours.
Also, given that both the taps can together fill the tank in  75 8 hr.  
So, the tap with a smaller diameter can fill 1/x part of the tank in 1 hour. Similarly, the tap with a larger diameter can fill (x−10) of the tank in 1 hour. Also, both the taps fill  8 75   part of the tank in 1 hour.
Then, we have
Question Image x =25, 4x =15 or x= 15 4  
When x =25, (x-10) = 25-10 = 15
When  x= 15 4  , (x-10) = 15 4 −10= 15−40 4 = −25 4  
Since, the time can never be negative so  x= 15 4   is rejected.
Hence, x = 25 and (x-10) = 15
Hence, the correct answer is 1) 25
 
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