A box contains some pomegranates, mangoes and oranges. 0.2 of the pomegranates is equal to 70% of the mangoes. The number of oranges is ²₃ of the total number of mangoes and pomegranates. If there are 36 more oranges than mangoes, how many fruits are there in the box altogether?

Pomegranates	Mangoes	Oranges
7x1	2x1
3x3		2x3
7 u	2 u	6 u

0.2 = ²₁₀= ¹₅
70% = ⁷⁰₁₀₀ = ⁷₁₀

0.2 of the pomegranates is equal to 70% of the mangoes. Make the numerators the same.  LCM of 1 and 7 is 7.

1x75x7 of the pomegranates = 7x110x1 of the mangoes
735 of the pomegranates = 710 of the mangoes 

Pomegranates : Mangoes
35 : 10 _(÷5)
7 : 2

The total number of pomegranates and mangoes is repeated.  Make the total number of pomegranates and mangoes the same.  LCM of 9 and 3 is 9.

Number of more oranges than mangoes
= 6 u - 2 u
= 4 u

4 u = 36

1 u = 36 ÷ 4 = 9

Number of the fruits in the box altogether
= 7 u + 2 u + 6 u
= 15 u
= 15 x 9
= 135

Answer(s): 135