Question

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

Answer 1

Let these two numbers be X and Y, Y being the bigger number. Then as per the question, 

X + Y = 25  .....(i) 

2Y² = 3X² + 29 ..... (ii) 

From (i), we get Y= 25 - X. Putting this in (ii), we get 

2{25-X)² = 3X² + 29 

⇒ 1250 + 2X² -100X= 3X² + 29 

⇒ X² + l OO X - 1221 = 0 

⇒ X² - 11 X +111X - 1221 = 0 

⇒ X (X - 11) +111( X - 11) = 0 

⇒ (X-11) (X+111) = 0 

⇒ X can't be a negative number and hence X=11 

⇒ X=11, hence Y = 14 .