A box contains some persimmons, mangosteens and kiwis. 0.6 of the persimmons is equal to 80% of the mangosteens. The number of kiwis is ³₅ of the total number of mangosteens and persimmons. If there are 42 more kiwis than mangosteens, how many fruits are there in the box altogether?

Persimmons	Mangosteens	Kiwis
4x5	3x5
5x7		3x7
20 u	15 u	21 u

0.6 = ⁶₁₀= ³₅
80% = ⁸⁰₁₀₀ = ⁴₅

0.6 of the persimmons is equal to 80% of the mangosteens. Make the numerators the same.  LCM of 3 and 4 is 12.

3x45x4 of the persimmons = 4x35x3 of the mangosteens
1220 of the persimmons = 1215 of the mangosteens 

Persimmons : Mangosteens
20 : 15 _(÷5)
4 : 3

The total number of persimmons and mangosteens is repeated.  Make the total number of persimmons and mangosteens the same.  LCM of 7 and 5 is 35.

Number of more kiwis than mangosteens
= 21 u - 15 u
= 6 u

6 u = 42

1 u = 42 ÷ 6 = 7

Number of the fruits in the box altogether
= 20 u + 15 u + 21 u
= 56 u
= 56 x 7
= 392

Answer(s): 392