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Question
A two digit number is such that the product of the digits is 14. When 45 is added to the number, then the digit are reversed. Find the number.
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Solution
Let these two numbers be X and Y, Y being the bigger number. Then as per the question,
X + Y = 25 .....(i)
2Y2 = 3X2 + 29 ..... (ii)
From (i), we get Y= 25 - X. Putting this in (ii), we get
2{25-X)2 = 3X2 + 29
⇒ 1250 + 2X2 -100X= 3X2 + 29
⇒ X2 + l OO X - 1221 = 0
⇒ X2 - 11 X +111X - 1221 = 0
⇒ X (X - 11) +111( X - 11) = 0
⇒ (X-11) (X+111) = 0
⇒ X can't be a negative number and hence X=11
⇒ X=11, hence Y = 14 .
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