# 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 1^{st}generation be x, then number of bacteria in 2

^{nd}, 3

^{rd}, 4

^{th}. . . . . 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)}