Problem Solving

A company producing fruit juice changed its packaging from boxes measuring 5 x 10 x 20 centimeters to boxes measuring 6 x 10 x 20 centimeters. If the price of a box did not change and all boxes are full of juice, by approximately what percent did the price of the juice decrease?

A. 12.00%
B. 16.67%
C. 18.33%
D. 20.00%
E. 21.50%

OA: B

Hi richachampion,

Start with calculating the 2 volumes:

V1 = 5 x 10 x 20 = 1000 cubic cm
V2 = 6 x 10 x 20 = 1200 cubic cm

Assume that the price remains unchanged at $1000 (just as an example and not as a ridiculously priced juice )

When you calculate a per unit cost, the difference in cost will come through.

Scenario 1: With V1 being sold for $1000, per unit cost would be 1000/1000 = $1 per cu. cm
Scenario 2: With V2 being sold for $1000, per unit cost would be 1000/1200 = $5/6 per cu. cm

Now calculate the change in the per unit price and the percentage change on the original base:
Change in price = 5/6 - 1 = - $1/6
Original price = $1
Percentage change = -1/6 / 1 x 100 = -1/6 x 100 = -16.67%

So, the price of the juice has dropped by 16.67% which is covered by Option B.