Question

7 times a two digit number is 4 times the number with its digits inversed .find the number if the sum of the digits is 3

Answer 1

let two digit number be 10x + y and it's reversed two digit number is 10y + x

7 times a two digit number is 4 times the number with its digits inversed
so, 7(10x + y) = 4(10y + x)
7(9x + (x + y) ) = 4(9y + (x + y))...........(1)

the sum of the digits is 3
so, x + y = 3.........(2)

substitute (2) in (1)
7(9x + 3) = 4(9y + 3)
7*3(3x + 1) = 4*3(3y + 1)
7(3x + 1) = 4(3y + 1)
21x + 7 = 12y + 4
21x + 7 - 4 = 12y
21x + 3 = 12y
3(7x + 1) = 3*4y
7x + 1 = 4y
y = (7x + 1)/4............(3)

substitute (3) in (2)
x + ((7x + 1)/4) = 3
(4x + 7x + 1)/4 = 3
11x + 1 = 12
11x = 12 - 1
11x = 11
x = 1

substitute x in (2)
1 + y = 3
y = 3 - 1
y = 2

so, the two digit number is 10x + y = 10*1 + 2 = 10 + 2 = 12

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