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Question

A two-digit positive number is such that the product its digits is 8. If 18 is added to the number then the digits are reversed, then the original number is


Solution

Let the two digit number be pq
Now, given conditions
p×q=8q=8p(1)
And
(10p+q)+18=10q+p
qp=2
Using equation (1), we get
8pp=28p2=2pp2+2p8=0p2+4p2p8=0(p2)(p+4)=0p=2,4
As the number is positive, so
p=2q=4

Hence, the original number is 24

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