IIT JEE , AIEEE Forum - Mathematics , Algebra

eistien

In a season lasting 50 days, every day some chrysanthemum flowers bloom on a tree. On the first day if ?n? flowers bloomed and on the next day all the flowers that bloomed on the previous day except one fell off. (No flower fell off on the first day). If the number of flowers that fell off on the second day is 5 and it is known that on any given day in that season the difference between the number of flowers that bloomed on that day and that of the number of flowers that fell off on that day is constant.

In that period of 50 days, how many flowers bloomed to that tree?

How many flowers fell off in the first 25 days?

On which of the following days 166 flowers bloom on the tree?

learner

Two questions

a) Do the same number of flowers bloom everyday?

b)Was the tree full on the first day?

eistien

the question is self explainatory try it out!!!! it was given in a bitsat sample test!!!!

shreyasnivas

bloody hell..

allamraju

The answers are 1)6425 2)1500 3)33.If my ans are correct,I will explain.

eistien

yes you are right plz explain and give full solution!!!!

allamraju

Though the problem looked difficult,it is basically a problem on A.P.Let no. of flowers bloomed be n_b and those fallen be n_f.Given,n_b-n_f=k(a constant)

No.of flowers that fell second time=5 means those that bloomed first time are 6.So,

k=6-0=6=n_b2-n_f2n_b2=11 $\Rightarrow$ n_f3=10 $\Rightarrow$ n_b3=16 and so on since it is given that flowers that fell this time is equal to those that bloomed previous time-1.

So,the no.of flowers bloomed are 6,11,16,21,.... and those that fell are 0,5,10,15,.....

Now,for first question,it is sum to 50 terms of first A.P.

for 2nd Q,it is sum to 25 terms of second A.P

for 3rd one,166=6+(n-1)5 gives the ans as 33.

eistien

PERFECT SOLUTION!!!! CHEERS