Consider two natural numbers, 'a' and 'b', which are in the ratio of 17:20. If we increase 'a' by 18 and decrease 'b' by 20, the new ratio of 'a' to 'b' becomes 6:5. Determine the square of the difference between 'a' and 'b'.
Let values of 'a' and 'b' be '17y' and '20y'. respectively. ATQ, (17y + 18) ÷ (20y - 20) = (6/5) Or, 5 X (17y + 18) = 6 X (20y - 20) Or, 85y + 90 = 120y - 120 Or, 35y = 210 Or, 'y' = 6 Required square of difference between two numbers: = (20y - 17y) 2 = (3y) 2 = (3 X 6) 2 = 182 = 324
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