GATE CSE
First time here? Checkout the FAQ!
x
+1 vote
96 views

There are 10 bacteria in a flask. Every hour 3 bacteria die and the remaining ones are each divided into 2 after 1 day, how many bacteria will live there?
Assume that the flask is large enough to contain any number of bacteria?

  1.   226
  2.   226 + 6
  3.   224 + 6
  4.   224
asked in Combinatory by Veteran (12.6k points)   | 96 views

226 + 6 ?

yes,your answer is correct,,how did you get that??

1 Answer

+1 vote
Best answer
hours bacteria alive difference
1 (10-3)*2 = 14  
2 (14-3)*2 = 22 22-14 = 8
3 (22-3)*2 = 38 38-22 = 16
4 (38-3)*2 = 70 70-38 = 32

.

.

.

.

   

from above table we found that

after 2 hours bacteria = 14 + 2= 22

after 3 hours bacteria = 14 + 23 + 24 = 38

after 4 hours bacteria = 14 + 23 + 24 + 25= 70

.

.

.

so after k hours bacteria = 14 + 23 + 24 + 2+ ........ + 2k+1

put value of k as 24

baacteria = 14 + 23 + 24 + 2+ ........ + 225

                   = 7 + 1 + 2 + 22 + 23 + 24 + 2+ ........ + 225

              = 7 + 226 - 1

              = 226 + 6

answered by Boss (7.7k points)  
selected by

thanks for the above solution..

can we solve this using recursion?

like i was solving like this but could 'nt proced further-

an+1 = 2(an - 3)

so,an =( an+1/2) + 3

an+1 = (an+2/2) + 3 putting this in an,we get a= (an+2 / 22) + 3/2 + 3

.

.

.

solving o..we get

an = a n + k /2 + 3( 1+ 1/2 + 1/22 + ....... + 1/ 2k-1)

now,i dun know how to solve further

i was taking base condition as a10 = 14..but i did nt lead me anywhere..can u pls help

Related questions



Top Users Mar 2017
  1. rude

    5246 Points

  2. sh!va

    3054 Points

  3. Rahul Jain25

    2920 Points

  4. Kapil

    2732 Points

  5. Debashish Deka

    2602 Points

  6. 2018

    1574 Points

  7. Vignesh Sekar

    1440 Points

  8. Bikram

    1432 Points

  9. Akriti sood

    1420 Points

  10. Sanjay Sharma

    1128 Points

Monthly Topper: Rs. 500 gift card

21,553 questions
26,902 answers
61,258 comments
23,269 users