Question

A vessel contains 180 litres of milk , 60 litres are taken out of the vessel everyday & equal quantity of

water is added. What quantity of milk remains in the vessel at the end of 3 days ?

a. 59 5/7 litres b. 65 1/5 litres

c. 53 1/3 litres d. 61 7/9 litres

Answer 1

X is the quanity of milk  and y is taken and add water and n is number of days x(1−y/x)ⁿ = 180( 1 - 60/180)³ = 180(2/3)³ = 180 x 8/27 = 160/3 = 53  1/3 litres

Answer 2

Question:  A vessel contains 180 litres of milk , 60 litres are taken out of the vessel everyday & equal quantity of  water is added. What quantity of milk remains in the vessel at the end of 3 days ?

Solution:

Day1: Initially it had 180L of milk. But then, 60 litres are taken out of the vessel everyday & equal quantity of  water is added. So, it'll have:

Quantity of milk = 180(1-60/180)^1 L

Day2: 60L taken out i.e. 30L water and 30L milk also 60L water added so, resulting solution will have:

Quantity of milk = 180(1-60/180)^2 L

Day3: 60L taken out i.e. 30L water and 30L milk also 60L water added so, resulting solution will have:

Quantity of milk = 180(1-60/180)^3 L = 160/3 = 53.33 i.e. Option C is the correct answer.