Question

A two-digit number is such that the product of its digits is 14. When 45 are added to the number, then their digits are reversed. Find the number.

Answer 1

The answer for your question is 27.

Verification:
27 = 2 × 7 = 14.
27 + 45 = 72. (digits are reversed)

Hope it helps you.

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Answer 2

Solution :

Let ten's place digit = x ,

unit place digit = y

Original Number = 10x + y ---( 1 )

Reverse the digits we get new

number = 10y + x ------( 2 )

Given product of digits = 14

=> xy = 14 ----( 3 )

According to the problem given ,

we get

10x + y + 45 = 10y + x

=> 10x - x + y - 10y = -45

=> 9x - 9y = -45

Divide each term by 9 , we get

=> x - y = -5 -----( 4 )

Now ,

( x + y )² = ( x - y )² + 4xy

= ( -5 )² + 4 × 14 [ from ( 4 )&( 3 ) ]

= 25 + 56

= 81

( x + y ) = 9 -----( 5 )

Add ( 4 ) & ( 5 ), we get

2x = 4

=> x = 2

Put x = 2 in equation ( 3 ) , we get

y = 7

Therefore ,

Original Number = 10x + y

= 10×2 + 7

= 27

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