A box contains some mangoes, persimmons and mangosteens. 0.2 of the mangoes is equal to 80% of the persimmons. The number of mangosteens is ¹₃ of the total number of persimmons and mangoes. If there are 4 less persimmons than mangosteens, how many fruits are there in the box altogether?

Mangoes	Persimmons	Mangosteens
4x3	1x3
3x5		1x5
12 u	3 u	5 u

0.2 = ²₁₀= ¹₅
80% = ⁸⁰₁₀₀ = ⁴₅

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

1x45x4 of the mangoes = 4x15x1 of the persimmons
420 of the mangoes = 45 of the persimmons 

Mangoes : Persimmons
20 : 5 _(÷5)
4 : 1

The total number of mangoes and persimmons is repeated.  Make the total number of mangoes and persimmons the same.  LCM of 5 and 3 is 15.

Number of less persimmons than mangosteens
= 5 u - 3 u
= 2 u

2 u = 4

1 u = 4 ÷ 2 = 2

Number of the fruits in the box altogether
= 12 u + 3 u + 5 u
= 20 u
= 20 x 2
= 40

Answer(s): 40