Numbers and

Question

8 litres are drawn from a container full of juice and is filled with water. This operation is performed 3 more times. The ratio of the quantity of juice now left in the container to that of water is 16:81. How much mango juice did the container hold originally? 

Answer 1

There are 4 stages of dilution, each by ratio d so we have d⁴  = 16/81. Taking 4th root, d = 2/3.

 

2/3 of original container became water at first stage and this was 8 litres.

 

(2/3) (original juice) = 8 litres of water, so (3/2)(8) = 12 litres, all juice, originally.