Question

the sum of digit of a two digit number is 7. The number obtained by interchaging the digit exceeds the original number by 27. find the number

Answer 1

let the ones digit be x
and tens digit be y
therefore the number is (10y+x)
ATQ,
x+y = 7 .......(1)
by second condition
(10x+y) - (10y+x) = 27
9x - 9y = 27
x - y = 3
x = y+3 ......(2)
putting value of x in eq(1) we get
y+3+y = 7
2y = 4
y =2
putting value of y in eq(2) we get
x = 2+3
x = 5
therefore the number is (10(2)+5) = 20+5 = 25
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