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Let us assume the initial stock of all the fruits is S.
Let us take we have 'b' and 'a' mangoes initially.
Stock of Mangoes = 40% of S = 2S/5
The total number of fruits sold are Mangoes Sold + Apples Sold + Bananas Sold
= 2S/10 + 96 + 4a/10 = S/2 (Given)
S/5 + 96 + 2a/5 = S/2
S = (4a + 960)/3
4a/3 + 320
'a' has to be a multiple of 3 for the above term to be an integer.
But 'a' has to be a multiple of 5 for 4a/10 to be an integer.
The smallest value of 'a' satisfying both conditions is 15.
4a/3 + 320 = 4(15)/3 + 320 = 340