Henry bought some passion fruits and dragonfruits in the ratio of 1 : 5 . After buying another 78 fruits each, the ratio becomes 7 : 9. Find the number of passion fruits and dragonfruits he has now.

	Passion Fruits	Dragonfruits	Difference
Before	1x1 = 1 u	5x1 = 5 u	4x1 = 4 u
Change	+ 78	+ 78
After	7x2 = 14 u	9x2 = 18 u	2x2 = 4 u

Since the same number of fruits bought for each type of fruits is the same, the difference in the number of passion fruits and dragonfruits at first and in the end remains unchanged. 

Make the difference in the number of passion fruits and dragonfruits the same. LCM of 4 and 2 is 4.

Increase in the number of passion fruits
= 14 u - 1 u
= 13 u

13 u = 78

1 u = 78 ÷ 13 = 6

Number of dragonfruits and passion fruits that $(Fred) has now
= 14 u + 18 u
= 32 u
= 32 x 6
= 192

Answer(s): 192