If 201 digits were used to number the pages of a book, starting from 1, find the number of pages in the book.

Do pls share your logic friends

The capital of a company, Estyle, is made of 75,000 preferred shares with a dividend of 15% and 20,000 common shares, with the par value of each type of share as Rs 10. The total profit of Estyle was Rs 2,40,000 of which Rs. 40,000 was kept in a reserve fund. The remaining profit was distributed to the shareholders. What would be the difference in the dividend percentage given to the common shareholders if the amount kept away in the reserve fund was reduced to Rs 25,000?

#XAT #Funda #2011

-Amiya

https://38.media.tumblr.com/700b49158f61ca7318ebc69db232a3bb/tumblr_ngz1c0CPcR1tcrq1uo1_1280.jpg

## FRACTIONAL PART AND INTEGRAL PART

R=(5*rt5+11)^2n+1 find fractional part of this number .

let f is fractional part of this f=R-[R]

let a number X=(5*rt5-11)^2n+1

X will lie in 0

so R-X=(5*rt5+11)^2n+1-(5*rt5-11)^2n+1

so R-X=2*(2n+1c1*(5*rt5)^2n*11+2n+1c3*(5rt5)^2n-2* (11)^3......

so R-X=even number

so [R]+f-X=even

so f-X=even-[R]

so f-X=an integer (odd or even both possible)

so f-X=0

bcz 0

0

so f-X=0

so f=X=(5rt5-11)^2n+1

so fractional part is (5rt5-11)^2n+1

___________________________________________________________________________________________

2nd question

R=(5+2*rt6)^n=[R]+f

let X=(5-2rt6)^n

so[R}+f+X=((5+2*rt6)^n+(5-2rt6)

so R+f+G=2*(nc0*5^n+nc2*5^n-2*(2rt6)^2....

so [R]+f+X=even

so f+X=integer

so f+X=1

so f=1-x so 1-(5-2rt6)^n________________________

Note - 1) in R=(a+b*rtc)^kif k is odd then f=X

fractional part will be f=(a-b*rtc)^n

2) and if k is even then f+X=1

f=1-(a-b*rtc)^k

example )find greatest integer less than or equal to (rt2+1)^6

ANS- here n=6 means even

so f+X =1 so

f=1-x =1-(rt2-1)^6

so (rt2+1)^6 =integer+fraction

so integer=(rt2+1)^6-fraction

= (rt2+1)^6-(1-(rt2-1)^6

= (rt2+1)^6+(rt2-1)^6-1

Now solve (rt2+1)^6+(rt2-1)^6 by simple binomial expansion

so integer=198-1

=197

-By hunny malhotra

@harshcat91 sir thanks a lot for teaching so many concepts in a simpler way 😃 hope u nail it tom..all the very best ..u really deserve to be in iim a..

P.S. sir toh bolna banta hai 😛

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@shojazz phew ! done!

haan ab dikha ki funda kaha pe tha 😃 gud one 👍