A number consists of two digits. The sum of its digits is 16. If 28 is subtracted from the number, the digits interchange their place. Find the number. | Simultaneous Equations | SciPiPupil

Question: A number consists of two digits. The sum of its digits is 16. If 28 is subtracted from the number, the digits interchange their place. Find the number.

Solution:

Given,

Let the digit at tens place be x and the digits at ones place be y. The required number is 10x+y.

According to the question,

Condition I,

The sum of the digits is 16.

$or, x + y = 16$

$or, x = 16 - y$ - (i)

Condition II,

If 28 is subtracted from the number, the digits interchange their place.

$or, 10x + y - 18 = 10y +x$ 

$or, 10x - x -18 = 10y -y$

$or, 9x -18 = 9y$

Put value of x from equation (i) in equation (ii), we get,

$or, 9(16 - y) -18 = 9y$

$or, 144 - 9y -18 = 9y$

$or, 126 = 9y +9y$

$or, 18y = 126$

$or, 18×y = 18×7$

$\therefore y = 7$

Now,

Put the value of y in equation (i), we get,

$or, x = 16-7$

$\therefore x = 9$

So, (x,y) = (9,7)

10x = 10×9 = 90

10x +y = 90+7 = 97

Therefore, the required two digit number is 97.