The average of twelve numbers is 39. The average of the last five numbers is 35, and that of the first four numbers is 40. The fifth number is 6 less than the sixth number and 5 more than the seventh number. The average of the fifth and sixth numbers is:
The Sum of the twelve numbers = 12 × 39 = 468 The sum of the last five number = 5 × 35 = 175 The sum of the first four number = 4 × 40 = 160 The sum of the fifth, sixth and seventh number = (468 – 175 – 160) = 133 Let, the fifth number is x Then, the sixth number is (x + 6) and the seventh number is (x – 5) x + (x + 6) + (x – 5) = 133 ⇒ 3x + 1 = 133 ⇒ 3x = 132 ⇒ x = 44 The fifth number is 44 and the sixth number is (44 + 6) = 50 Average of fifth and sixth number is (44 + 50)/2 = 47
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