Three friends had dinner at a restaurant `2/3` When the bill was received, Alpana paid as much as Beena paid and Beena paid `1/2` as much as Catherin paid. What fraction of the bill did Beena pay?
Solution
Let ‘T’ be the total bill amount at the restaurant and ‘a’, ‘b’, and ‘c’ be the share of Alpana, Beena, and Catherin respectively.
Given, that Alpana paid rd `2^"rd"/3` as much as Beena paid
∴ a = `2/3`b ................(i)
Also, Beena paid `1/2` as much as Catherin paid.
∴ b = `1/2` c i.e. c = 2b ..................(ii)
∴ Three friends paid the total bill amount.
∴ a + b + c = T ..................(iii)
Using (i) and (ii) in (iii), we get
`2/3`b + b + 2b = T
∴ b`(2/3 + 1 + 2) = "T"`
∴ b`((2 + 3 + 6)/3)` = T
∴ `(11"b")/3` = T
∴ b = `3/11`T
Thus, Beena paid `(3/11)^"th"` fraction of the total bill amount.
