Question

The seed of a particular variety of a rose in a rose garden , multiplies into 2 everyday due to reproduction. If there is only one seed on the first day, it increases to two on the second day, increases to eight on fourth day and so on. If starting with one seed it takes 30 days to cover 200 meters plot, how long will it take to cover the same plot if started with two seeds ?

• A. $16$ days
• B. $15$ days
• C. $17$ days
• D. $29$ days

Answer 1

The correct option is D $29$ days

The roses are increasing the pattern,

$1,2,4,8,16$ and so on in each passing day. The given series is into Geometric Progression.

Common ratio of this GP,

$r=2/1=2$

Now, The sum of the given GP, taking one seed first day, i.e

$a=1$
Number of terms(n)$=30$ (as given number of days are 30.)

$Sum=a\times \frac{(r^n-1)}{(r-1)}$

$Sum=1\times \frac{(2^{30}-1)}{(2-1)}$

$Sum=1,07,37,41,823$
$1,07,37,41,823$ roses are needed to cover $200$ meters plot.

Now, in Second case, series would be like this:

$2,4,8,16,32$ and so on

$a=2$

$r=4/2=2$

$Sum=1,07,37,41,823$

Now, we have to find number of days, i.e $n$

$Sum=a\times \frac{(r^n-1)}{(r-1)}$

$1,07,37,41,823=2\times \frac{(2^n-1)}{(2-1)}$

On Solving we will get,
$n=29$ days.