Question
If (6x + y) = 180 and 5x:2y = 25:12, then find the
value of (2x² + 5y²).Solution
Given, 5x:2y = 25:12 Or, 5x × 12 = 2y × 25 Or, 60x = 50y So, x:y = 5:6 So, let the values of 'x' and 'y' be '5k' and '6k', respectively. ATQ, (6x + y) = 180 Or, 6 × 5k + 1 × 6k = 180 Or, 30k + 6k = 180 Or, 36k = 180 So, 'k' = 5 Therefore, values of 'x' and 'y' are 25 and 30, respectively. So, (2x² + 5y²) = (2 × 25² + 5 × 30²) = (2 × 625 + 5 × 900) = (1250 + 4500) = 5,750 Hence, option d.
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