Question

Date
Page
A two digit number is such that the
product of its digits is 14. If 45
is added to the number, the
digits interchage their places Find
the number
​

Answer 1

Answer:

let number be 10x+y

so x × y=14

so x=14/y and

10x +y+45=10y+x

45=9y-9x

y-x=5

y-14/y=5

y^2-14=5y

y^2-5y-14=0

y^2-7y+2y-14=0

y(y-7)+2(y-7)=0

(y+2)(y-7)=0

y=-2 or y=7

taking y=7 because digit is not negative

if y is 7 then x is 2

hence number 10x + y =10×2+7=27