A) \[Rs.\,\,42780\]
B) \[Rs.\,\,43690\]
C) \[Rs.\,\,43680\]
D) None of these
Correct Answer: B
Solution :
Firstly, one person post four letters to four of his friends. Then, those four persons post\[4-4\] letters \[i.e.,\] a total \[4\times 4=16\] letters. Similarly, in next step \[4\times 4\times 4=64\] letters are posted. Thus, there will be a \[GP\] series. \[i.e.,\] \[4,\,\,16,\,\,64,\,\,256,\,....\] where,\[a=4\]and\[r=4\] Now, total number of letters till 8th set \[{{S}_{n}}=\frac{a({{r}^{n}}-1)}{r-1}\] \[\Rightarrow \] \[{{S}_{n}}=\frac{4({{4}^{8}}-1)}{4-1}\] \[\Rightarrow \] \[{{S}_{8}}=\frac{4}{3}({{4}^{8}}-1)\] \[\left\{ \because \,\,{{S}_{n}}=\frac{\alpha ({{r}^{n}}-1)}{r-1},\,\,r>1 \right\}\] Cost of one letter\[=Rs.\,\,0.50\] Hence, total cost\[=\frac{4}{3}({{4}^{8}}-1)\times 0.50\] \[=\frac{4}{3}\times (65536-1)\times 0.50\] \[=\frac{4}{3}\times 65535\times 0.50\] \[=Rs.\,\,43690\]You need to login to perform this action.
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