The average number of mangosteens in Box H, Box J and Box K is 65 and it is 5 more than the average number of oranges in the 3 boxes. ¹₅ of the oranges are in Box H and the oranges in Box H is 80% of the number of oranges in Box J. If each box has the same number of fruits, what percentage of the fruits in Box K are mangosteens?
Average number of oranges
= 65 - 5
= 60

Total number of oranges
= 3 x 60
= 180

Total number of mangosteens
= 3 x 65 
= 195

Total number of fruits
= 180 + 195
= 375

Number of fruits in each box
= 375 ÷ 3
= 125

Oranges in Box H	Oranges in Box J	Oranges in Box K	Total oranges
1x4	4x4		5x4
4x1	5x1
4 u	5 u	11 u	20 u

80% = ⁸⁰₁₀₀ = ⁴₅

The number of oranges in Box H is repeated.  Make the number of oranges in Box H the same.  LCM of 1 and 4 is 4. 

Total number of oranges
= 4 u + 5 u + 11 u
= 20 u

20 u = 180

1 u = 180 ÷ 20 = 9

Number of oranges in Box K
= 11 u
= 11 x 9
= 99

Number of mangosteens in Box K
= 125 - 99
= 26

Percentage of the fruits in Box K are mangosteens
= ²⁶₁₂₅ x 100%
= 20.8%

Answer(s): 20.8%