Question

The sum of the digits of a two digit number is 13 if 27 is added to the number the digits get it interchanges what is the number

Answer 1

HELLO!!
SO YOUR ANS IS......

let the tens digit be x and unit digit be y

given that x + y = 13
y = 13 - x


no. is 10x + y

after interchanging we get no. as 10y + x

questions says that 27 is added to the number

this means 10x + y + 27 = 10y + x
= 10 x + y - 10y - x = -27
= 9x - 9 y = -27
= 9y - 9x = 27 (Taking 9 common)
= y - x = 3

now putting y = 13 - x
= (13 - x) - x = 3
= 13 - x - x = 3
= 13 - 2x = 3
= -2x = 3 - 13
= - 2x = -10
= - x = -10/2
= -x = - 5
= x = 5

So x = 5
y = 13 - x
y = 13 - 5
y = 8

Number is 58
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