Discussion

Explanation:

Let the amount Achal invested be Rs. P.

Amount due at the end of 3 years = $\mathrm{P}\times \left(1+\frac{5}{100}\right)\times \left(1+\frac{6}{100}\right)\times \left(1+\frac{7}{100}\right)$

Amount due at the end of 3 years had he invested at 6% = $\mathrm{P}\times {\left(1+\frac{6}{100}\right)}^3$

The difference = $\mathrm{P}\times {\left(1+\frac{6}{100}\right)}^3$ - $\mathrm{P}\times \left(1+\frac{5}{100}\right)\times \left(1+\frac{6}{100}\right)\times \left(1+\frac{7}{100}\right)$

= $\mathrm{P}\times \left(1+\frac{6}{100}\right)\left[{\left(1+\frac{6}{100}\right)}^2-\left(1+\frac{5}{100}\right)\left(1+\frac{7}{100}\right)\right]$

= $\mathrm{P}\times \left(\frac{106}{100}\right)\left[{\left(\frac{106}{100}\right)}^2-\left(\frac{105}{100}\right)\left(\frac{107}{100}\right)\right]$

= $\mathrm{P}\times \left(\frac{106}{100}\right)\left[\frac{{106}^2-(106-1)(106+1)}{{100}^2}\right]$

= $\mathrm{P}\times \left(\frac{106}{100}\right)\left[\frac{{106}^2-(106-1)(106+1)}{{100}^2}\right]$

= $\mathrm{P}\times \left(\frac{106}{100}\right)\left[\frac{{106}^2-{106}^2-1}{{100}^2}\right]$

= $\mathrm{P}\times \frac{106}{{100}^2}$

Given, $\mathrm{P}\times \frac{106}{{100}^2}$ = 3286

⇒ P = 3,10,000

Hence, option (c).

∴ ×

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