A box contains some mangosteens, persimmons and lemons. 0.2 of the mangosteens is equal to 60% of the persimmons. The number of lemons is ²₅ of the total number of persimmons and mangosteens. If there are 24 less persimmons than lemons, how many fruits are there in the box altogether?

Mangosteens	Persimmons	Lemons
3x5	1x5
5x4		2x4
15 u	5 u	8 u

0.2 = ²₁₀= ¹₅
60% = ⁶⁰₁₀₀ = ³₅

0.2 of the mangosteens is equal to 60% of the persimmons. Make the numerators the same.  LCM of 1 and 3 is 3.

1x35x3 of the mangosteens = 3x15x1 of the persimmons
315 of the mangosteens = 35 of the persimmons 

Mangosteens : Persimmons
15 : 5 _(÷5)
3 : 1

The total number of mangosteens and persimmons is repeated.  Make the total number of mangosteens and persimmons the same.  LCM of 4 and 5 is 20.

Number of less persimmons than lemons
= 8 u - 5 u
= 3 u

3 u = 24

1 u = 24 ÷ 3 = 8

Number of the fruits in the box altogether
= 15 u + 5 u + 8 u
= 28 u
= 28 x 8
= 224

Answer(s): 224