Explanation
For first two year interest $$= P\left [\left (1+\dfrac{R}{100}\right)^2-1\right] = 272$$ .......(1) For first three year interest $$= P\left [\left (1+\dfrac{R}{100}\right)^3-1\right] = 434$$ .......(2) On dividing equation (1) by (2), we get $$\Rightarrow\dfrac{ \left (1+\dfrac{R}{100}\right)^2-1 }{ \left (1+\dfrac{R}{100}\right)^3-1 }= \dfrac{272}{434}$$ Let $$\left (1+\dfrac{R}{100}\right)=x$$ ...........(3)
$$\Rightarrow \dfrac{(x^2-1)}{ (x^3-1) }= \dfrac{136}{217}$$ $$\Rightarrow \dfrac{(x+1)}{(x^2+x+1) }= \dfrac{136}{217}$$ $$136x^2-81x-81 = 0$$ After solving $$x$$ will be $$1.1248$$ By putting this value in eq (3), we get $$R = 12.48$$ approx $$12.50$$ $$\%$$
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