Latest Others Aptitude Question SOLUTION: if you place 9 in the left hand side of a 5-digit number, you get a 6-digit number.this 6-digit number is four times the 6-digit number that you get when you place 9 in the right h

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if you place 9 in the left hand side of a 5-digit number, you get a 6-digit number.this 6-digit number is four times the 6-digit number that you get when you place 9 in the right hand side of the original 5 digit number. what is the sum of the digits of the original 5-digit number? all digits are distinctly different. what are they?

Asked In Others K Praneetha (11 years ago)

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SDeep Bhattacharya  (11 years ago)

Let the 5-digit number is : ABCDE ;[ Where A,B,C,D,E are th digits of the 5-digit number ].
So, actually the 5-digit number is = (10^4)A +(10^3)B +(10^2)C + 10D + E

Now, by the given condition:
(9ABCDE)= 4*(ABCDE9)...[remember A,B,C,D,E are digits here and not multiplied]
Or, in another way,we can write
9*(10^5)+ (10^4)A +(10^3)B +(10^2)C + 10D + E =
4*{(10^5)A+ (10^4)B +(10^3)C +(10^2)D + 10E + 9}
Clearly A 9ABCD6 = 4*(ABCD69)....(eqn 1 )
nOW,4*(69)=276
so, the last 2-digits of 4*(ABCD69) will be (76).
So, from (eqn 1 )
we get 9ABCD6 = 4*(ABCD69)
So,D=7
=> 9ABC76 = 4*(ABC769)............[eqn 2]
Again we see that 4*(769)= 3076.
So, last 3 digits of 4*(ABC769) will be : (076)
So, we get from [eqn 2]
9ABC76 = 4*(ABC769)
where ,C=0
=> 9AB076 = 4*(AB0769)
we see that 4*(0769)=
last 4-digits of 4*(AB0769) will be (3076)
So, a similar argument as above gives that
from,
9AB076 = 4*(AB0769)
B=3
=>9A3076=4*(A30769)
Now, 4*(30769)=123076
So,applying a similar argument we get,
A=2 .
So, the original 5-digit number is : ABCDE = 23076.

To see whether it satisfies the condition or not, we observe that :
923076 = 4*(230769), which is actually correct.

So, original 5-digit number is : 23076 .

THANKS to All.. :-):-) ..

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SDeep Bhattacharya  (11 years ago)

CORRECTION OF PRINTING ERROR :-
----------------------------------------------------
in the above solution,
plse consider the equation where I mentioned (eqn 1)
there is a slight printing mistake, the (eqn 1) should be read as :

Clearly , 9ABCD6 = 4*(ABCD69)....(eqn 1 )

This is bcoz last digit of 4*(ABCDE9) will be =6 ; [since 4*9 = 36]
so,the last digit of (9ABCDE) will be 6;
So, E = 6...

Now refer to the rest part of the solution..

thanks to All..:-) :-)

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