A can contain 10l of pure milk. 2l of milk is drawn out and replaced by 2l water. The process is repeated four times. Now the ratio of milk to water in the can is: select one:
a. 369:256
b. 2:3
c. 1 : 9
d. 256:369
Answers
We will do this in steps :
When 2l of milk is drawn and replaced with 2l of water we have :
8l of milk and 2 l of water
The ratio is :
Milk : Water = 8 : 2
= 4 : 1
When 2 litres is drawn again.
the amount of : 1) Milk is = 8/10 × 2 = 1.6 litres
2) water = 0.4 litres
The new amounts :
6.4 litre of milk and 1.6 litres of water
when we add 2 litres of water we get 3.6 litres of water
The new ratio :
is : 16 : 9
We draw 2 litres again :
Amount of milk remaining = 6.4 - (16/25 × 2) = 5.12 litres
The amount of water remaining = 3.6 - (9/25 × 2) = 2.88 liters
We add 2 liters of water :
Milk = 5.12 Litres
Water = 4.88 litres.
The new ratio:
64 : 61
We draw 2l again.
Milk remaining = 5.12 - (64/125 × 2) = 4.096 liters
Water = 4.88 - (61/125 × 2) = 3.904
New amounts :
Milk = 4.096
water = 5.904
New ratios :
Milk : water
= 4.096/5.904 = 256 / 369
= 256 : 369