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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.

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Comments ( 3 )

  1. Rifat Mahmud
    Rifat Mahmud :
    3 years ago

    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.

  2. Suresh Yadav
    Suresh Yadav :
    3 years ago

    Why you didn't add remaining 50% in the next generation

  3. NEHA SHARMA
    NEHA SHARMA :
    4 years ago

    1/2%= 1/(2*100) = 0.005
    { Explanation: Example-
    5% =5/100 so 1/2% = 1/(2*100)}

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