Question 59

If (x + 4), (x + 12), (x - 1), and (x + 5) are in proportion then the mean proportional between x and (x - 7)is:

Solution

If (x + 4), (x + 12), (x - 1), and (x + 5) are in proportion

=> $$\frac{x+4}{x+12}=\frac{x-1}{x+5}$$

=> $$(x+4)(x+5)=(x-1)(x+12)$$

=> $$x^2+9x+20=x^2+11x-12$$

=> $$2x=20+12=32$$

=> $$x=\frac{32}{2}=16$$

Now, mean proportional of $$x$$ and $$(x-7)$$

= $$\sqrt{16\times9}=\sqrt{144}=12$$

=> Ans - (D)

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