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 8 th set of letter is mailed.

Answer 1

It is given that a person writes a letter to four friends and asks each friend to copy the letter and mail to four different persons with instruction that they have to move the chain similarly.

The number of letters mailed is in such a way that it forms a G.P.,

4+ 4 2 + 4 3 +....+ 4 8

Here, first term a=4, common ratio r=4 and number of terms n=8.

The sum of the G.P. is given by,

S n = a( r n −1 ) r−1

Substitute values of a, rand n in the above formula,

S n = a( r n −1 ) r−1 =4 ( 4 8 −1 ) 4−1 =4 ( 65535 ) 3 =87380

Now, 50 Paisa= 1 2  Rs

Now, cost for mailing 87830 letters is,

Cost=87380× 1 2 =43690

Thus, the amount spent on the postage when 8th set of letter was mailed is Rs.43690.