Question

The difference between a two digit number and the number obtained by interchanging the two digits of the number is 18. the sum of the two digit of the number is 12. what is the product of the two digit of the two digit number?

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\:\:$

$\green{\underline \bold{Given :}}$

$\:\:$

• The difference between a two digit number and the number obtained by interchanging the two digits of the number is 18

$\:\:$

• The sum of the two digit of the number is 12

$\:\:$

$\red{\underline \bold{To \: Find:}}$

$\:\:$

• Product of the two digit of the two digit number

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

Let the tens digit be 'x'

Let the ones digit be 'y'

$\:\:$

$\underline{\bold{\texttt{Original number :}}}$

$\:\:$

$\purple\longrightarrow$ $\sf 10x + y$

$\:\:$

$\underline{\bold{\texttt{Reversed number :}}}$

$\:\:$

$\purple\longrightarrow$ $\sf 10y + x$

$\:\:$

$\purple{\underline \bold{According \: to \: the \ question :}}$

$\:\:$

$\sf \longmapsto 10x + y -(10y + x) = 18$

$\:\:$

$\sf \longmapsto 10x + y - 10y - x = 18$

$\:\:$

$\sf \longmapsto 9x - 9y = 18$

$\:\:$

$\underline{\bold{\texttt{Dividing the above equation by 9}}}$

$\:\:$

$\sf \longmapsto x - y = 2$ -----(1)

$\:\:$

Also Given,

$\:\:$

Sum of the two digit of the number is 12

$\:\:$

$\purple\longrightarrow$ $\sf x + y = 12$ -----(2)

$\:\:$

$\underline{\bold{\texttt{Adding (1) \& (2)}}}$

$\:\:$

$\sf \longmapsto x - y + x + y = 2 + 12$

$\:\:$

$\sf \longmapsto 2x = 14$

$\:\:$

$\sf \longmapsto x = \dfrac { 14 } { 2 }$

$\:\:$

$\bf \dashrightarrow x = 7$

$\:\:$

$\underline{\bold{\texttt{Putting x = 7 in (1)}}}$

$\:\:$

$\sf \longmapsto 7 - y = 2$

$\:\:$

$\sf \longmapsto y = 7 - 2$

$\:\:$

$\bf \dashrightarrow y = 5$

$\:\:$

$\bf \dag \: \: Product \: = \: 7 \times 5$

$\:\:$

$\bf \dashrightarrow Product \: = \: 35$

$\rule{200}5$

Answer 2

Given:

The difference between a  two-digit number and the number obtained by interchanging the two digits is 18. The sum of the digits of the two numbers is 12.

To Find:

The product of the two digits of the two-digit number is?

Solution:

1. Let the initial two-digit number be 10x+y.

2. The difference between the initial number and the number formed by the interchanging digits is 18,

=> 10x + y - (10y + x) = 18,

=> 10x + y - 10y - x = 18,

=> 9x - 9y = 18,

=> x - y = 2, (Consider as equation 1).

3. The sum of the digits of the initial number is 12,

=> x + y = 12. (Consider as equation 2).

4. Solve equations 1 and 2 for the values of x and y

=> Add equations 1 and 2,

=> x - y + x + y = 2 + 12,

=> 2x = 14,

=> x = 7.

5. Substitute the value of x in equation 1,

=> 7 - y = 2,

=> y = 7 - 2,

=> y = 5.

6. Therefore the number formed is 7x10+5 = 75.

=> The product of the two digits of the initial number is 7 x 5 = 35.

Therefore, the product of the two digits of the two-digit number is 35.