A box contains some oranges, persimmons and apples. 0.2 of the oranges is equal to 40% of the persimmons. The number of apples is ³₅ of the total number of persimmons and oranges. If there are 12 less persimmons than apples, how many fruits are there in the box altogether?

Oranges	Persimmons	Apples
2x5	1x5
5x3		3x3
10 u	5 u	9 u

0.2 = ²₁₀= ¹₅
40% = ⁴⁰₁₀₀ = ²₅

0.2 of the oranges is equal to 40% of the persimmons. Make the numerators the same.  LCM of 1 and 2 is 2.

1x25x2 of the oranges = 2x15x1 of the persimmons
210 of the oranges = 25 of the persimmons 

Oranges : Persimmons
10 : 5 _(÷5)
2 : 1

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

Number of less persimmons than apples
= 9 u - 5 u
= 4 u

4 u = 12

1 u = 12 ÷ 4 = 3

Number of the fruits in the box altogether
= 10 u + 5 u + 9 u
= 24 u
= 24 x 3
= 72

Answer(s): 72