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? Choose the correct choice from the following choices:
A) 2
B) 9
C) 1.8
D) 1.7
E) None
Explanation :   Jan 1 – S1 and S2 has n members. Till july 2nd, there are 6 more months, and hence 6 more additions.   In S1, b members are added each month. So after 6 months, S1 has n + 6b.   In S2, r members are multiplied each month. So after 6 months, S2 has n * r6.   After 6 months, both are same, hence   =&gt; n + 6= 
<gadget id="calculator">+ 6</gadget>
<output>6</output>
nr6. ----------------- (1)=&gt; b = 10.5 n. (given)   =&gt; 6b = 63n hence.   Substituting in (1)   So, 64n = nr6. Cancelling n on both sides, we have r6 = 64 or r = 2.   2nswer : 2
<result>A</result>
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?