A box contains some passion fruits, lemons and mangosteens. 0.2 of the passion fruits is equal to 80% of the lemons. The number of mangosteens is ¹₂ of the total number of lemons and passion fruits. If there are 27 less lemons than mangosteens, how many fruits are there in the box altogether?

Passion Fruits	Lemons	Mangosteens
4x2	1x2
2x5		1x5
8 u	2 u	5 u

0.2 = ²₁₀= ¹₅
80% = ⁸⁰₁₀₀ = ⁴₅

0.2 of the passion fruits is equal to 80% of the lemons. Make the numerators the same.  LCM of 1 and 4 is 4.

1x45x4 of the passion fruits = 4x15x1 of the lemons
420 of the passion fruits = 45 of the lemons 

Passion Fruits : Lemons
20 : 5 _(÷5)
4 : 1

The total number of passion fruits and lemons is repeated.  Make the total number of passion fruits and lemons the same.  LCM of 5 and 2 is 10.

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

3 u = 27

1 u = 27 ÷ 3 = 9

Number of the fruits in the box altogether
= 8 u + 2 u + 5 u
= 15 u
= 15 x 9
= 135

Answer(s): 135