A container contains some pears, mangosteens and apples. 0.2 of the pears is equal to 80% of the mangosteens. The number of apples is ⁵₈ of the total number of mangosteens and pears. If there are 102 more apples than mangosteens, how many fruits are there in the container altogether?

Pears	Mangosteens	Apples
4x8	1x8
8x5		5x5
32 u	8 u	25 u

0.2 = ²₁₀= ¹₅
80% = ⁸⁰₁₀₀ = ⁴₅

0.2 of the pears is equal to 80% of the mangosteens. Make the numerators the same.  LCM of 1 and 4 is 4.

1x45x4 of the pears = 4x15x1 of the mangosteens
420 of the pears = 45 of the mangosteens 

Pears : Mangosteens
20 : 5 _(÷5)
4 : 1

The total number of pears and mangosteens is repeated.  Make the total number of pears and mangosteens the same.  LCM of 5 and 8 is 40.

Number of more apples than mangosteens
= 25 u - 8 u
= 17 u

17 u = 102

1 u = 102 ÷ 17 = 6

Number of the fruits in the container altogether
= 32 u + 8 u + 25 u
= 65 u
= 65 x 6
= 390

Answer(s): 390