Question

It takes 30 minutes to empty a half-full tank by draining it at a constant rate. it is decided to simultaneously pump water into the half-full tank while draining it. what is the rate at which water has to be pumped in so that it gets fully filled in 10 minutes?

Answer 1

lets say capacity of tank is 1 litre
draining rate= 0.5litre/30minutes= 1/60 litre/min
let filling rate = x litre/min
in 1 min tank gets x-(1/60) litre filled.
to fill the remaining half part we need 10mins
x-1/60 litre --> 1min
0.5 litre ---> 10 mins
0.5/(x-1/60) = 10
solving, we get x= 4/60
which is 4 times more than draining rate.

Answer 2

let

A = 30m     30/30=1Unit                             L.C.M = 30,10 = 30

.'.  We need to fill the upper half (30 Unit)  in 10m.

B-A = 10m      30/10 = 3Unit   

=> B-A = 3

=> B-1 =  3

=>B = 3+1 = 4    (ANSWER)