Question

the sum of the digits of a two-digit number is 7. if 9 is added to the number it's digits are reversed. find the number.

Plz help me...
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Answer 1

let the digit be x and y

so the no. is

$10x + y$

ACTQ,

$x + y = 7 - - - - (1)$

and,

$10x + y + 9 = 10y + x$

$9x + 9 = 9y$

$x + 1 = y - - - - (2)$

by using eq. 1 and 2,

$x + x + 1 = 7$

$2x </strong><strong>+</strong><strong> </strong><strong>1 = 7$

$2x = 6$

$x = 3$

using x=3 in eq. 2

$y = 3 + 1$

$y = 4$

so the no. is,

$10x + y = 10 \times 3 + 4$

$= 30 + 4$

$= 34$

Answer 2

Let the numbers be x and y

Eq.(1)

=> 10x + y

=> x + y = 7

=> 10x + y + 9 = 10y + x

=> 9x + 9 = 9y

=> x + 1 = y

Eq.(2)

=> x + x + 1 = 7

=> 2x + 1 = 7

=> 2x = 6

=> x = 2/6

=> x = 3

Eq.(3)

=> y = 3 + 1

=> y = 4

Final Eq.

=> 10x + 10 × 3 + 4

=> 30 + 4

=> 34

Therefore, the number = 34

Hope it helps!!!