Question 63

If x is added to each of 12, 28, 21 and 45, the numbers so obtained, in this order, are in proportion. What is the mean proportional between (x +3) and (4x+ 1)?

Solution

As per the given condition in the question,

$$\dfrac{12+x}{28+x}=\dfrac{21+x}{45+x}$$

$$\Rightarrow (12+x)(45+x)=(28+x)(21+x)$$

$$\Rightarrow 12\times 45 +12x+45x+x^2=28\times 21+28x+21x+x^2$$

$$\Rightarrow 57x-49x=588-540$$

$$\Rightarrow 8x=48$$

Hence x=6.

Mean proportional of the (x +3) and (4x+ 1) $$=\sqrt{(x+3)(4x+1)}$$

Substituting the value of x

$$=\sqrt{(x+3)(4x+1)}=\sqrt{9\times25}=3\times5=15$$

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