Question
Three numbers are given, where one-third of the first
number, two-fifths of the second number, and three-fourths of the third number are all equal. The difference between the second and third numbers is 98. Determine the average of the first and third numbers.Solution
Let the three numbers be 'a', 'b' and 'c' respectively.
ATQ, (a/3) = (2b/5) = (3c/4) = 'k'
So, 'a' = 3k, 'b' = (5k/2) and 'c' = (4k/3)
Now, (5k/2) - (4k/3) = 98
Or, (7k/6) = 98
So, 'k' = 84
Therefore, required average = (1/2) X {3k + (4k/3) }
= (1/2) X (13k/3) = (13k/6)
= (13 X 84) ÷ 6 = 182
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