The average number of persimmons in Box J, Box K and Box L is 45 and it is 10 more than the average number of mangosteens in the 3 boxes. ¹₅ of the mangosteens are in Box J and the mangosteens in Box J is 30% of the number of mangosteens in Box K. If each box has the same number of fruits, what percentage of the fruits in Box L are persimmons?
Average number of mangosteens
= 45 - 10
= 35

Total number of mangosteens
= 3 x 35
= 105

Total number of persimmons
= 3 x 45 
= 135

Total number of fruits
= 105 + 135
= 240

Number of fruits in each box
= 240 ÷ 3
= 80

Mangosteens in Box J	Mangosteens in Box K	Mangosteens in Box L	Total mangosteens
1x3	4x3		5x3
3x1	10x1
3 u	10 u	2 u	15 u

30% = ³⁰₁₀₀ = ³₁₀

The number of mangosteens in Box J is repeated.  Make the number of mangosteens in Box J the same.  LCM of 1 and 3 is 3. 

Total number of mangosteens
= 3 u + 10 u + 2 u
= 15 u

15 u = 105

1 u = 105 ÷ 15 = 7

Number of mangosteens in Box L
= 2 u
= 2 x 7
= 14

Number of persimmons in Box L
= 80 - 14
= 66

Percentage of the fruits in Box L are persimmons
= ⁶⁶₈₀ x 100%
= 82.5%

Answer(s): 82.5%