A two digit number is such that the product of its digits is 14.the number obtained by interchanging the digits is 45 less than the original number. Find the original number.
Answers
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Let the one's place of the two digit number be x and the ten's place of the two digit number be y.
Given, x*y=14----equation 1
Now; original number=10*y + x----equation 2
new number=number obtained by interchanging the digits=10*x + y----equation 3
(interchanging the digits means the one's place digit is interchanged with the ten's place digit and the vice-versa)
According to the question,
new number=original number - 45
(from equations 2 and 3)
=>10*x + y=10*y + x- 45
=>9*x - 9*y+45=0
=>9(x-y+5)=0
=>x-y+5=0
Also from equation 1, x=14/y
so, 14/y -y+5=0
=>14-y^2+5 y=0
=>y^2-5 y -14=0
on factorizing, we get y=7 or y=-2
here , if we take y =7, then x=2 and original number will be 72;
if we take y=-2, then x=-7 and original number will be -27