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=8⇒q=8p⋯(1) And (10p+q)+18=10q+p ⇒q−p=2 Using equation (1), we get ⇒8p−p=2⇒8−p2=2p⇒p2+2p−8=0⇒p2+4p−2p−8=0⇒(p−2)(p+4)=0⇒p=2,−4 As the number is positive, so p=2⇒q=4 Hence, the original number is 24

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