Question

A two digit number is such that the sum of its digits is 14.If the digits are reversed the new number exceeds the old one by 36.find the original number

Answer 1

Answer:

59

Step-by-step explanation:

Let

The unit digit of the number be x

& Tens digit of the number be y

So the two digit number will be 10y + x

Now on reversing the digits, the new number formed will be 10x + y

So according to the question,

(10x + y) - (10y + x) = 36

= 10x - x + y - 10y = 36

= 9x - 9y = 36

= x - y = 4...... (i)

Also given that

X + y = 14....(ii)

Subtracting eq (i) from (ii) we get

(X + y) - (x - y) = 14 - 4

= x + y - x + y = 10

= 2y = 10

= y = 10/2 = 5

&

X + y = 14

So

X = 14 - 5 = 9

So the original number is 59

&

New number is 95

Answer 2

Answer:

$\boxed{\sf \: Number \: = \: 59 \: }$

Step-by-step explanation:

$\begin{gathered}\begin{gathered}\bf\: Let-\begin{cases} &\sf{digit \: at \: ones \: place \: be \: y} \\ \\ &\sf{digit \: at \: tens \: place \: be \: x} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf\: So-\begin{cases} &\sf{Number \: formed \: = \: 10x + y} \\ \\ &\sf{Reverse \: number \: = \: 10y + x} \end{cases}\end{gathered}\end{gathered}$

According to statement, sum of the digits of a two digit number is 14.

$\sf \: x + y = 14$

$\sf\implies \sf \: y = 14 - x - - - (1)$

According to statement, the reverse number exceeds the original number by 36.

$\sf \: 10y + x - (10x + y) = 36$

$\sf \: 10y + x - 10x - y = 36$

$\sf \: 9y - 9x= 36$

$\sf \: 9(y - x)= 36$

$\sf \: y - x = 4$

On substituting the value of y from equation (1), we get

$\sf \: 14 - x - x = 4$

$\sf \: 14 - 2x = 4$

$\sf \: - 2x = 4 - 14$

$\sf \: - 2x = - 10$

$\sf\implies \sf \: x = 5$

On substituting the value of x = 5 in equation (1), we get

$\sf\implies \sf \: y = 14 - 5= 9$

Hence,

$\sf \: Number \: \: = \: 10 \times 5 + 9$

$\sf\implies \bf \: Number \: = \: 59$