Latest Others Aptitude Question SOLUTION: The square of a two digit number is divided by half the number. After 36 is added to the quotient, this sum is then divided by 2. The digits of the resulting number are the same as

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The square of a two digit number is divided by half the number. After 36 is added to the quotient, this sum is then divided by 2. The digits of the resulting number are the same as those in the original number, but they are in reverse order. how many such no r there

Asked In Others sanjeev (12 years ago)

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Abhishek Sharma  (12 years ago)

let the digits be x and y. then the number is 10x+y
given: (10x+y)^2/[(10x+y)/2]=2(10x+y).
[2(10x+y)+36]/2=10y+x
or, 10x+y+18=10y+x
or, 9y=9x+18
or, y=x+2
therefore, 10x+y=13,24,35,46,57,68,79

Is this solution Helpfull? Yes (54) | No (7)  

tejaswini g  (11 years ago)

let the two digit number be xy
so....
square of the number is (xy)^2
half of the number is (xy)/2
the quotient for the ... square of the number divided half of the number is 2xy
according to problem
(36+quotient)/2=yx
we already got quotient=2xy
(36+2xy)/2=yx

by solving we get xy-yx=18.........(1)
for example 52
we can write it as 5*10+2
in the same way we can write eq(1) as
(10x+y)-(10y+x)=18
y-x=2
31,42,53,64,57,68,79

I

Is this solution Helpfull? Yes (11) | No (6)  

Dr.Dipin Singh  (12 years ago)

if xy is the number , resulting number is xy+18 =yx
It is possible when y =x+2

Such numbers are
13,24,35,46 , 57 ,68,79

Is this solution Helpfull? Yes (9) | No (3)  

Vadivelan M  (12 years ago)

7 such numbers are there. They are 13,24,35,46,57,68,79.

Is this solution Helpfull? Yes (6) | No (7)  

faizanqureshi  (8 years ago)

suppose two digit number is =xy
The square of a two digit number is =(xy)2
Then it divided by half the number =(xy)2/(xy/2)=2(xy)
After 36 is added to the quotient =2xy+36
This sum is then divided by 2 =(2xy+36)/2 = (xy)+18
If we take 46 from the given option =(46)+18=64
Note:The digits of the resulting number are the same as those in the original number, but they are in reverse order.

Is this solution Helpfull? Yes (1) | No (1)  

Saurabh Mandal  (8 years ago)

Ans is 7
Explanation : ((xy)^2)/(xy/2) =(2xy +36)/2= xy +18
Now putting x=0 ,y=2 we get 02+ 18 = 20(not accepted becoz 02 is not 2 digit no)
then x=1,y=3 we get 13 + 18= 31
like this 24,35,46,57,68,79
So the total nos are 7

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