Question

Sum of the digits of a two digit number is 7.When we interchange the digits of this
number, it is found that the resulting number is greater than the original number by 25.
Find the original number

Answer 1

Step-by-step explanation:

Let the units place be x

and tens place be y

Original number = x + 10y

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

After interchange,

units place = y

and tens place =x

Interchanged number = y + 10x

According to the question,

Interchanged number = Original number + 25

y + 10x = x + 10y + 27

10x - x + y - 10y = 27

9x - 9y = 27 -----(2)

Solve (1) and (2) by elimination method, we get,

(1) -》

9x + 9y = 63

9x - 9y = 25

------------------

18x = 90

x = 90/18

x = 5

when x = 5, (1) gives

5 + y = 7

y =2

hence units place = 5

tens place = 2

number = 2×10 + 5×1

= 25