VeritasPrepKarishma wrote:
The original question is:
A strain of bacteria reproduces at the rate of 25% every 12 min. In how much time will it triple itself ?
a) 96 min
b) 72 min
c) 60 min
d) 48 min
e) 40 min
Responding to a pm:
If initial amount of bacteria is X, we need it to become 3X. How many 12 min time intervals does it need? Let's assume we need n time intervals.
X*(5/4)^n = 3X
(5/4)^n = 3
Now note that the options are 12*4, 12*5, 12*6 etc. So this gives us some ideas.
(5/4)^4 = 625/256 -> this is much less than 3 since 256*3 is more than 750.
(5/4)^5 = 3125/1024 -> this is a tiny bit more than 3 and hence is out answer since 1024*3 is a bit more than 3000.
Hence n is 5 and time required = 12*5 = 60 mins
Why cant we use GP Series here?? Can you please clarify.
Let x be initial bacteria. Now, we have
x + 5x/4 + 25x/16 + ... = 3x
(5/4)^n = 7/4..
However, I am not able to get value of n here.