Question

Q.2 A two digit number is such that product of its digits is 14. When 45 is added to
this number, the digits interchange their places. Find the numbers.​

Answer 1

Answer:

Step-by-step explanation:

Let's take a Digit x and y

When x×y=14

Therefore when 45 is added to the product of it's digit the answer is yx

14+45=72

Hence X=2 and Y=7

The Digit is 27

Answer 2

Answer:

27

Step-by-step explanation:

Let the digits be a and b such that the number is 10a+b.

ab = 14

and ,

==> 10a + b + 45 = 10b + a

==> 9a - 9b = -45

==> a - b = 5 eq 1

$Now \: \\ {a + b}^{2} = ({a - b}^{2} ) + 4ab \\ \\ {a + b}^{2} \: = 25 + 4 \times 14 = 81 \\ \\ (a + b) = 9 \: \: \: \: \: \: eq \: 2$

From eq 1 and eq 2 , we get. ,

a = 2 ; b = 7

Hence ,

the number is 27 .