A box contains some passion fruits, mangoes and lemons. 0.2 of the passion fruits is equal to 70% of the mangoes. The number of lemons is ²₃ of the total number of mangoes and passion fruits. If there are 32 less mangoes than lemons, how many fruits are there in the box altogether?

Passion Fruits	Mangoes	Lemons
7x1	2x1
3x3		2x3
7 u	2 u	6 u

0.2 = ²₁₀= ¹₅
70% = ⁷⁰₁₀₀ = ⁷₁₀

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

1x75x7 of the passion fruits = 7x110x1 of the mangoes
735 of the passion fruits = 710 of the mangoes 

Passion Fruits : Mangoes
35 : 10 _(÷5)
7 : 2

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

Number of less mangoes than lemons
= 6 u - 2 u
= 4 u

4 u = 32

1 u = 32 ÷ 4 = 8

Number of the fruits in the box altogether
= 7 u + 2 u + 6 u
= 15 u
= 15 x 8
= 120

Answer(s): 120