Given, Average of x occurring 5 times and y occurring 7 times is 37 . ⇒5x+7y=37×(5+7) ⇒5x+7y=37×12 . . . (i) Average of x occurring 7 times and y occurring 5 times is 35 ⇒7x+5y=35(7+5) . . . (ii) From Eq. (i) and Eq. (ii), (5x+7y=37×12)×7 and (7x+5y=35×12)×5 We get, 35x+49y=37×12×7 −35x±25y=−35×12×5 ⇒24y=12(37×7−35×5) ⇒24y=12×84 ∴y=42