The average number of mangosteens in Box S, Box T and Box U is 20 and it is 8 more than the average number of starfruits in the 3 boxes. ¹₆ of the starfruits are in Box S and the starfruits in Box S is 30% of the number of starfruits in Box T. If each box has the same number of fruits, what percentage of the fruits in Box U are mangosteens?
Average number of starfruits
= 20 - 8
= 12

Total number of starfruits
= 3 x 12
= 36

Total number of mangosteens
= 3 x 20 
= 60

Total number of fruits
= 36 + 60
= 96

Number of fruits in each box
= 96 ÷ 3
= 32

Starfruits in Box S	Starfruits in Box T	Starfruits in Box U	Total starfruits
1x3	5x3		6x3
3x1	10x1
3 u	10 u	5 u	18 u

30% = ³⁰₁₀₀ = ³₁₀

The number of starfruits in Box S is repeated.  Make the number of starfruits in Box S the same.  LCM of 1 and 3 is 3. 

Total number of starfruits
= 3 u + 10 u + 5 u
= 18 u

18 u = 36

1 u = 36 ÷ 18 = 2

Number of starfruits in Box U
= 5 u
= 5 x 2
= 10

Number of mangosteens in Box U
= 32 - 10
= 22

Percentage of the fruits in Box U are mangosteens
= ²²₃₂ x 100%
= 68.75%

Answer(s): 68.75%