Question

From a container, 6 litres milk was drawn out and was replaced by water. Again 6 litres of mixture was drawn out and was replaced by the water. Thus the quantity of milk and water in the container after these two operations is 9 : 16. The quantity of mixture is :

Answer 1

Let quantity of mixture be x litre
Now since 6 litre milk is drawn and operation is repeated 2 times
if we repeat 1 time we get (x-6), the formula used here is if we draw y litre and operation is repeated n times
So mixture left=
So milk left
=
Now given milk:water=9:16
=> milk:(milk+water)=9:(9+16)
=>milk: mixture=9:25
So we have,

x(1 - 6/x)2 /x = 9/25
=> (1 - 6/x)2=9/25
=> (1 - 6/x)2=(3/5)2
=>1 - 6/x=3/5
=>6/x=1 - 3/5
=>6/x=2/5
=>2x=30
=>x=15
So quantity of mixture is 15 litre