# 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

2015-05-10T08:05:15+05:30
let the original no. be 10x+y,where,x is in the tenths place and y in the unit's place.

so the no obtained by interchanging the digits= 10y+x

GIVEN
x + y = 12

10y + x = 10x + y + 18

So,
10y - y = 10x - x + 18

9y = 9x +18
as all three are multiples of 9,we get: y = x + 2

by substituting the value of y in x+y =2, we get:
x+ x+2 = 12

2x=10,

x = 5

hence, y =12-x =12-5 =7

by this, we can conclude that the original no. is 57 which is 18 lesser than 75

plss mark as the best if it was helpful...
2015-05-10T14:58:18+05:30
Let the original number be x y.(x at ten's place and y at units place)
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
57 AND THE OTHER NO IS 75