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There are 2 taps to fill a big tank; one is bigger & other is smaller. A bigger alone can fill up the tank in 5 hours less than smaller tap can alone. Both taps together take 6 hours to fill up the tank.
How many hours required separately for smaller & bigger taps to fill up the tank?
Click here for answer!
What was the question?
Let x be hours required for bigger tap then smaller needs x + 5
hours.
In
1 hour bigger fills 1/x & smaller fills 1/(x+5) part of the tank.
Together both take 6 hours to completely fill the tank. So,
1/x + 1/(x+5) = 1/6
6(x + 5 + x) = x^2 + 5x
x^2 - 7x - 30 = 0
(x-10) (x+3) = 0
x + 3 = 0 gives x = -3 which is not possible as x represents hours.
So x - 10 = 0 gives x = 10.
Hence for a bigger tap 10 hours & for smaller tap 10 + 5 = 15 hours required to fill up the tank!
You have 12 black socks and 12 white socks mixed up in a drawer. You’re
up very early and it’s too dark to tell them apart. What’s the smallest
number of socks you need to take out (blindly) to be sure of having a
matching pair?
To know what it is click here!
Source
Question is here!
You need only 3 attempts.
Let's say on first draw we get BLACK socks. In next draw, if we get BLACK then we have matching pair immediately. But if in second draw, it's WHITE then we have to go for third draw.
On a third draw, if it's BLACK then we have pair of BLACK socks ; one came from first draw & other from third one!
On the other hand, if we get WHITE on third draw then we have pair of WHITE socks ; one we got from second & other from third.
Same logic can be applied if WHITE comes in first draw.
