Question : What smallest positive number should be subtracted from 2 and 3 so that 4 is the third proportion to them?
Option 1: 1
Option 2: 2
Option 3: 4
Option 4: 3
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Correct Answer: 1
Solution :
Let the number subtracted be $x$.
$(2-x)$ : $(3-x)$ :: $(3-x)$ : $4$
⇒$\frac{(2-x)}{(3-x)} = \frac{(3-x)}{4}$
⇒$(3-x)^2 = 4(2-x)$
⇒ $x^2-6x+9 = 8-4x$
⇒ $x^2-2x+1=0$
⇒ $(x-1)^2=0$
⇒ $x = 1$
Hence, the correct answer is 1.
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