Question 55

If (x + y):(x - y) = 5:2, find value of (4x + 5y) / (x - 4y)

Solution

Given : $$\frac{x + y}{x - y} = \frac{5}{2}$$

=> $$2x + 2y = 5x - 5y$$

=> $$2y + 5y = 5x - 2x$$ => $$7y = 3x$$

=> $$y = \frac{3x}{7}$$

To find : $$\frac{4x + 5y}{x - 4y}$$

= $$[4x + 5(\frac{3x}{7})] \div [x - 4(\frac{3x}{7})]$$

= $$(4x + \frac{15x}{7}) \div (x - \frac{12x}{7})$$

= $$(\frac{43x}{7}) \div (\frac{-5x}{7})$$

= $$\frac{43x}{7} \times \frac{-7}{5x} = \frac{-43}{5}$$

=> Ans - (C)

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