Question

sum of the digit of a 2 digit no. is 10.when we interchanged the digits it is found that the resulting new no.is greater than the original no.by18. find the original number

Answer 1

Let the digits of 2-digit no. be (xy)

{note that they are not multiplied}
[x is in tens' place and y is in units place
so place value of x is 10&place value of y is 1]

given
sum of digits is 10
x+y = 10 -------------------------(1)


Digits are interchanged
No. = (yx)

Also given, (10y+x)= (10x+y)+18
9y=9x+18
=>-9x+9y= 18--------------------(2)

do (2)÷9
-x+y= 2 ----------------------------(3)

do (1) + (3)
2y=12
=>y=6

x=10-y
x=10-6
=>x=4

Thus original no. is (xy)= 46

Check:
Sum of digits of 46=10
when interchanged new no. is 64
64-46= 18
...Verified...

Hope it helps . ^_^
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