# Q.the sum of 2 digit no is 12.if the digits are interchanged,the resulting no is 18 more than the original no.find the original no.?

2
by cnirmalkar

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by cnirmalkar

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x+ x+2 = 12

2x=10,

x = 5

Therefore, the number can also be 10x+y.

New number after interchanging the digits=y x.

This number can also be 10y+x.

Given,

10y+x-10x-y=18

or,9y-9x=18

or,x-y=2...............(2)

Also given , x+y=12...........(1)

Subtracting equation (2) from equation (1) we get=

x+y-(x-y)=12-2

or,x+y-x+y=10

or,2y=10

or,y=5.

Since x+y=12

x+5=12 or, x=7.

Therefore, the original number is