On January 1, 2004 two new societies, S1, and S2, are formed, each with n members. On the first day of each subsequent month, S1 adds b members while S2 multiplies its current number of members by a constant factor r. Both the societies have the same number of members on July 2, 2004. If b = 10.5n, what is the value of r?
Explanation:
Members are added on the first day of every month for 6 months before July 2, 2004.
Number of members in S1 on July 2, 2004 = n + 6b = 64n (as b = 10.5n)
Number of members in S2 on July 2, 2004 = n × r6
By conditions, 64n = n × r6
∴ r = 2
Hence, option (a).
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