The average of first three numbers of a set of six numbers is 60 .The average of the second, third and fourth numbers is 20 and the average of the third, fourth and fifth numbers is 30. The average of last three numbers is 40. What is the average of first three and last three numbers of the set?

Let the six numbers be a, b, c, d, e, f. a + b + c = 3 x 60 =180⟹ (1) b + c + d = 3 x 20 = 60⟹ (2) c + d + e = 3 x 30 = 90⟹ (3) d + e + f = 3 x 40 = 120⟹ (4) Sum of the first three and last three numbers is obtained by taking (1) + (3) – (2) - (4) a +b + c+ c +d + e –b – c – d –c – d – e =180 + 90 – 60 - 120 ⟹ a + b + c + d + e + f = 90 Average of a, b, c, d, e, and f = 90/6=15

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