Question

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

• A. 72
• B. 27
• C. 37
• D. 14

Answer 1

The correct option is B 27

Let the digits be a and b such that the number is 10a+b.
$\therefore$ ab =14 and 10a + b+ 45 = 10b + a
i.e., 9a - 9b = -45
i.e., a - b = -5
$(a+b{)}^2=(a-b{)}^2+4ab=25+4\left(14\right)=81$
$\therefore a+b=9$
$\therefore a=2,b=7$
$\therefore$ The number is 27.