Question
Coins are distributed among Anoop, Bishnu, Chinky, and
Danny such that the difference between Chinky’s share and Danny’s share is equal to the difference between Anoop’s share and Bishnu’s share. Additionally, Bishnu’s share and Chinky’s share are in the ratio 2:3, and Anoop’s share and Danny’s share are in the ratio 5:4. Determine the ratio of the shares of Anoop, Bishnu, Chinky, and Danny, respectively.Solution
ATQ, Let shares of Anoop, Bishnu, Chinky and Danny are ‘p’, ‘q’, ‘r’ and ‘s’ respectively. So, (p – q) = (r – s) ---------(1) q/r = 2/3 ---------(2) And, p/s = 5/4 ---------(3) From equations (1), (2) and (3): (p – q) = (3q/2) – (4p/5) p + (4p/5) = (3q/2) + q 9p/5 = 5q/2 p/q = 25/18 Let Anoop’s and Bishnu’s shares be ‘25a’ and ‘18a respectively. So, Chinky’s share = 18a × (3/2) = 27a And Danny’s share = 25a × (4/5) = 20a Required ratio = 25a: 18a: 27a: 20a = 25: 18: 27: 20
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