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A person writes a letter to four of his friends. He asks each one of them to copy the letter and mail to four different persons with instruction that they move the chain similarly. Assuming that the chain is not broken and that it costs 50 paise to mail one letter. Find the amount spent on the postage when $8^{\text {th }}$ set of letter is mailed.
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Verified Answer
The number of letters posted will form a G.P. $4,16,64$, $256 \ldots \ldots \ldots$ $a=4, \quad r=4$
No. of total letters mailed upto $8^{\text {th }}$ set of letters
$\begin{aligned}
&=S_8=\frac{a\left(r^8-1\right)}{(r-1)}=\frac{4\left(4^8-1\right)}{4-1}=\frac{4}{3}(65536-1) \\
&=\frac{4}{3} \times 65535=87380
\end{aligned}$
Postages spent@50 paise per letter
$=₹ \frac{50}{100} \times 87380=₹ 43690$
No. of total letters mailed upto $8^{\text {th }}$ set of letters
$\begin{aligned}
&=S_8=\frac{a\left(r^8-1\right)}{(r-1)}=\frac{4\left(4^8-1\right)}{4-1}=\frac{4}{3}(65536-1) \\
&=\frac{4}{3} \times 65535=87380
\end{aligned}$
Postages spent@50 paise per letter
$=₹ \frac{50}{100} \times 87380=₹ 43690$
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