There were 124 persimmons and passion fruits altogether. After ⁴₅ of the persimmons and half of the passion fruits were given away, there were a total of 41 persimmons and passion fruits left. What fraction of the fruits were passion fruits at first? Give your answer in its simplest form.

	Persimmons	Passion Fruits	Total
Before	5 u	2 p	124
Change	- 4 u	- 1 p	- 83
After	1 u	1 p	41

Number of persimmons and passion fruits given away
= 124 - 41
= 83

4 u + 1 p = 83
1 p = 83 - 4 u --- (1)

1 u + 1 p = 41
1 p = 41 - 1 u --- (2)

(2) = (1)
41 - 1 u = 83 - 4 u
4 u - 1 u = 83 - 41
3 u = 42

1 u = 42 ÷ 3 = 14

Number of persimmons at first
= 5 u
= 5 x 14
= 70

Number of passion fruits at first
= 124 - 70
= 54

Fraction of the fruits that were passion fruits at first
= ⁵⁴₁₂₄
= ²⁷₆₂

Answer(s): ²⁷₆₂