Question

the sum of the digits of a two digits number is 10 . if the number formed by reversing the digits is greater than the original number by 36, find the original number.
answer is 37
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Answer 1

Answer:

The number can be 37 or, 73

Step-by-step explanation:

Let the ones digit be x and tens digit be y

Their sum is 10 (given)

So, x + y = 10........eq.(i)

The number can be formed is

(10*x) + (y*1)

= 10x + y

Interchanging the digits :

10y + x

According to the question :

$\sf : \implies \: (10x + y ) - (10y - x) = 36 \\ \sf : \implies \: 9x - 9y = 36 \\ \sf : \implies \: 9(x - y) = 36 \\ \sf : \implies \: x - y = \frac{36}{9} \\ \sf : \implies \: x - y = 4 ......eq.(ii)$

Now,

Substraction of both the equation :

$\sf \: x + y = 10 \\ { \sf{ \underline{ \: x - y = 4}}} \\ \sf : \implies \: 2x = 6 \\ \sf : \implies \: x = \frac{6}{2} \\ \sf : \implies \: x = 3 \: ans.$

Substituting the value of x in equation (ii) :

$\sf : \implies \: x + y = 10 \\ \sf : \implies 3 + y = 10 \\ \sf : \implies \: y = 10 - 3 \\ \sf : \implies \: y = 7 \: ans.$

Hence,

The number is :

10x + y = (10*3) + (7*1) = 30 + 7 = 37 or, 73