Answers

2014-10-06T12:12:32+05:30
Let the number on the ten's place be 'x' nad unit place be 'y'

So when it is divided by the sum of the digit, the quotient is  7 :-

10x + y / x + y = 7 so,
3x - 6y = 0 ----------( equation 1)

Then, If 27 is sub from the no the digits are reversed:

10 x + y - 27 = 10 y + x
x - y = 27 ------------( equation 2)

Multiply Eq (1) and Eq (2), we get,

3x - 3y = 9-------------( 3)

Sub Eq (1) and (), we get

3x - 6y  = 0 - ( 3x - 3y = 9)
= 3y = 9
y = 9/3
= 3
( y = 3)-------( 4)

Put (4) in (2)
 
x - 3 = 27
x = 6

( x = 6)

So the number is 63





 


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2014-10-06T12:14:06+05:30

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Let x is the tenth digit and y is unit digit.
then the number is 10x+y.

When it is divided by sum of the digits, quotient is 7

thus  \frac{10x+y}{x+y} =7

10x+y=7x+7y
10x-7x=7y-y
3x=6y
x=2y

When 27 is subtracted from it, digits are reversed(y comes to tenth place and x goes to unit place), thus

(10x+y)-27=10y+x
10x-x=10y-y+27
9x=9y+27
x=y+3     (dividing by 9)
2y=y+3
2y-y=3
y=3
x=2y=2*3=6

The number is 10x+y = 10*6+3 = 63
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