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Question
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 8th set of letter is mailed.
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Solution
The first person writes four letters. The 4 people who receive the letter then write four letters each. In this way, the chain keeps increasing.
Numbers of letters on each occasion up to 4, 16, 24, …… to 8 terms
Total number of papers = 4 + 16 + 64 + …… to 8 terms
= `(4(4^8 - 1))/(4 - 1)`
= `4/3 (65536 - 1)`
= `4/3 xx 65535`
= 87380
Postage cost of one letter = 50 paise = `1/2` Rs.
total postage cost = `87380 xx 1/2`
= 43690 Rs.
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