Question

A two digit number is such that the product of its digits is 18. when 63 is subtracted from the number, the digits interchange their places. find the number ​

Answer 1

Answer:

92

Step-by-step explanation:

(10x + y) is a two-digit number

xy = 18

10x + y - 63 = 10y + x

9x - 9y = 63

x - y = 7

Digits are 9 and 2 and number is 92

Answer 2

Given:-

• The product of its digits of a two digits number is 18.
• When 63 is subtracted from the number, the digits interchange their places.

To find:-

• Find the original number.?

Solutions:-

• Let the digits at ten's place be x.
• Let the digits at the unit's place by y.

Number = 10x + y

The product of its digits of a two digits number is 18.

=> xy = 18 .........(i).

When 63 is subtracted from the number, the digits interchange their places.

=> 10x + y - 63 = 10y. + x

=> 10x + y - 10 - x = 63

=> 9x - 9y = 63

=> 9(x - y) = 63

=> x - y = 63/9

=> x - y = 7

=> x = 7 + y ........(ii).

Putting the value of x from Eq 2 in Eq 1

=> xy = 18

=> (7 + y)y = 18

=> 7y + y² = 18

=> y² + 7y - 18 = 0

=> y² + 9y - 2y - 18 = 0

=> y(y + 9) - 2(y + 9) = 0

=> (y - 2) (y + 9) = 0

=> y = 2 or y = -9 (neglected)

Putting the value of y in Eq 2. We get,

=> x = 7 + y

=> x = 7 + 2

=> x = 9

So, Number => 10x + y

=> 10 × 9 + 2

=> 90 + 2

=> 92

Hence, the original number formed is 93.