Question

the sum of digits of a two digit number is 7 .if the digits are reversed ,the new number is decreased by 2 equal twice the original number.find the number




someone answer fast plz

Answer 1

Let the two digit number be 10 x + y
sum of its digits = x + y = 7
If the digits are reversed the new number formed is decreased by 2 is equal to twice the original number
⇒ 10 y + x - 2 = 2(10 x + y)
10 y + x - 2 = 20 x + 2 y
20 x - x + 2 y - 10 y = -2 
19 x - 8 y = - 2

Simultaneous equation  x + y = 7
                                  19 x - 8 y = - 2
 19(x + y = 7)
 19 x - 8 y = - 2
 
 19 x + 19 y = 133→a
 19 x - 8 y = - 2→b
On subtracting  b from a   19 x + 19 y = 133
                                          - 19 x + 8 y = 2
27 y = 135
y = 5
On substituting y = 5 in x + y = 7 we get x = 2
Therefore the number is 10 x + y = 10(2) + 5 = 25