One bacterium splits into eight bacteria of the next generation. But due to environment, only 50% of one generation can produced the next generation. If the seventh generation number is 4096 million, what is the number in first generation?
A. 1 million
B. 2 million
C. 4 million
D. 8 million
E. None of these
Answer: Option A
Solution(By Examveda Team)
Let the number of bacteria in the 1st generation be x, then number of bacteria in 2nd, 3rd, 4th . . . . . Generation would be $$8\left( {\frac{{\text{x}}}{2}} \right),\,8\left( {\frac{{4{\text{x}}}}{2}} \right),\,8\left( {\frac{{16{\text{x}}}}{2}} \right)$$ . . . . And so on. As x, 4x, 16x, 64x . . . . . it is in GP with common ratio 4 Hence, 7th term of GP, x(4)6 = 4096 or, x = 1 or 1 million.Join The Discussion
Comments ( 3 )
Related Questions on Percentage
A. $$\frac{1}{4}$$
B. $$\frac{1}{3}$$
C. $$\frac{1}{2}$$
D. $$\frac{2}{3}$$
back solve,
6th year=4096/4=1024.
5th "=1024/4=256.
4th"=256/4=64.
3rd"=64/4=16.
2nd"=16/4=4.
1st"=4/1=1milion.
Why you didn't add remaining 50% in the next generation
1/2%= 1/(2*100) = 0.005
{ Explanation: Example-
5% =5/100 so 1/2% = 1/(2*100)}