A machine costing \(\operatorname{Rs} 3,00,000\) will have its scrap value of \(\operatorname{Rs} 50, 000\). The company at present plans to put \(\operatorname{Rs} 36, 650\) per annum at the end of each year in a sinking fund at the rate \(5 \%\) per annum for the replacement of the machine after its useful life. Suppose the new machine will cost \(\operatorname{Rs} 4,00,000\) at that time, then the useful life (approx.) of the machine is :
[Given: \((1.4775)^{\frac{1}{8}} \approx 1.05\) ]

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.