Question
The average of 10 numbers is 21.6. The average of the
first four numbers is 17.5, and the average of the last three numbers is 24. The fifth number is 6 less than the sixth number, which itself is 8 less than the seventh number. What is the average of the fifth and sixth numbers?Solution
Sum of fifth, sixth and seventh numbers = 21.6 X 10 - 17.5 X 4 - 24 X 3= 216 - 70 - 72 = 74Let the seventh number be 'p'.Sixth number = p - 8Fifth number = p - 8 - 6 = p - 14So, p + p - 8 + p - 14 = 74Or, 3p - 22 = 74Or, 3p = 96Or, 'p' = 32Required average = (p - 8 + p - 14) ÷ 2 = p - 11 = 32 - 11 = 21
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