Question

Trupti works for 8 days in a store. The store owners have two choices for a payment. She can get rupees 1 on the first day, rupees 2 on the second day, rupees 4 on the third day, rupees 8 on the 4th day and soon on. The second option is that she can get rupees 200 in all this payment. Which option will earn more money for and by how much more

Answer 1

if she get 1,2,4,8...
the terms are in GP
so for 8th day the amount is a8=a(r power7)
a8 = 1(2 power 7)
a8 = 128
so in days she earns the money = 1+2+4+8+..+128
so of terms in GP =
a((r power n) -1)/(r - 1)
sum =
1((2power 8) - 1)(2 - 1)
sum = 256 - 1 = 255
so by taking daily wages she can earn more money
I.e. 255>200