Question

the sum of a two digit number is 7. the number obtained by interchanging the digits exceeds the original number by 27. find the numbers

Answer 1

let the units place be x
then the tens digit be 7 - x
number formed by these digits = 10 x t's digit+u's digit
=> 10(7-x)+x
70 x -10 x +x
70 x -9x
when the digits are interchanged than,
t's digit= x
u's digit = 7-x
the new no. formed = 10x + 7-x
= 9 x +7
given that the no. exceeds by 27
new no. - given no.
9x +7 - (70-9x)=27
9 x + 7 - 70 + 9x =27
18x -63= 27
18 x = 63+27
18 x= 90
x = 90/18
=5
the no. = 70- 9x 
=> 70-45
=> 25 ans
verify : 2+5 = 7

@skb

Answer 2

hii mate here is the answer to your question
let the digit in the ones place be x and the digit in in the tens place be y
Therefore according to the question x+y=7.....(i)
The original no.=10×y+x=10y+x
The no. obtained by interchanging the digits =10x+y.
By the given condition, 10x+y=10y+x+27
or, 10x+y-10y-x=27
or, 9x-9y =27
or, (x-y) = 27/9=3.....(ii)
adding (i)and (ii,) we get
x+y=7
x-y=3
---------
2x=10
or, x=5
or, 5+y=7
or, y =2
therefore the number is 25
and no. obtained by interchanging the digits = 52
hope this helps
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