Question

A person sends an SMS to four friends with the instruction that it has to be sent to four of their friends. Considering the fact that the chain is not broken and that it costs 50 paise to send one message, find the amount spent when the eighth set of messages is sent.

• A. ₹ 73,690
• B. ₹ 44,690
• C. ₹ 43,698
• D. ₹ 43,690

Answer 1

The correct option is D

₹ 43,690

Number of messages sent in each set is given by -

1st set - 4 messages (sent by 1 person)

2nd set - 16 messages ($(4\times 4=16)$ sent by 4 persons)

3rd set - 64 messages ($(16\times 4=64)$ sent by 16 persons)
and so on.

Hence, the number of messages sent from 1st set to the 8th set are given by the sequence
4, 16, 64, 256,....... (upto to 8 terms).
This sequence of numbers forms a G.P., whose first term $a=4$ and common ratio $r=\frac{16}{4}=\frac{64}{16}=4.$
The total no. of messags sent in 8 sets is given by,
$S_8=\frac{a(r^n-1)}{r-1}=\frac{4(4^8-1)}{4-1}=\frac{4}{3}\times 65535$
$=87380$
Total cost of sending the messages @50 paise per message
$=50\text{paise}\times 87380=₹\frac{1}{2}\times 87380=₹43,690$
Hence, the amount spent in messaging is ₹43,690.