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The average marks obtained by Sunil in 6 subjects is 88. On subsequent verification, it was found that the marks obtained by him in a subject was wrongly copied as 86 instead of 68. The correct average marks obtained by him is $$(ab)_{10}$$, that is a two-digit number in base 10. Then $$a^2 + b^2 =$$
The recorded total is $$6 \times 88 = 528$$, and correcting the entry gives $$528 - 86 + 68 = 510$$. The correct average is $$\frac{510}{6} = 85$$, so $$a = 8$$ and $$b = 5$$. Hence $$a^2 + b^2 = 64 + 25 = 89$$.
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