# The sum of the digits of two-digit number is 9. If 27 is subtracted from the number, the digits are reversed. find the number.

2
by dweejareddy

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by dweejareddy

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Digit in units place = y

The number is 10x + y

Sum of digits = x + y = 9 ....(1)

If 27 is subtracted from the number, the digits are reversed.

10x + y - 27 = 10y + x

⇒ 9x - 9y = 27

⇒ x - y = 3 ........(2)

Solving equations (1) and (2)

We get, x = 6 and y = 3

the number is 63

given x+y = 9 --------- (1)

when 27 is subtracted,

10x+y-27 = 10y+x

9x-9y-27 = 0

x-y = 3 ----------- (2)

from (1) & (2)

x+y = 9

x--y = 3

-------------

2x = 12

x = 6

sub x = 6 in (1)

x+y = 9⇒ 6+y = 9

y= 3

required no (10x+y) = 10(6)+3

= 63